text:
Prolog by Example. - A predicate may have several alternative definitions (both facts and rules).
- Shawn Wood
- 2 years ago
- Views:
1 Prolog by Example - A Prolog program is composed of predicates defined by facts and rules, which are special cases of definite (or Horn) clauses, i.e. clauses with at most one positive literal (the head of the clause). - A predicate may have several alternative definitions (both facts and rules). - A fact has no negative literals and expresses positive knowledge that is definite (no disjunctions). Example: The knowledge that John is a child of Ann and Alex, and that Ann is a child of Bob, is expressed by two facts, namely child_of(john, ann). child_of(john, alex). child_of(ann, bob). - A rule has one or more negative literals (the body of the clause), and is used to infer predicates from other predicates. Example: A grand child is the child of the child, i.e. grand_child_of(x,y) :- child_of(x,z), child_of(z,y). - The name rule is due to the fact that a definite clause, H B 1 B 2... B k can be written in the form of an if expression H B 1 B 2... B k, which is the syntax adopted in Prolog. Foundations of Logic and Constraint Programming 1
2 Prolog by Example child_of(john, ann). child_of(john, alex). child_of(ann,bob). grand_child_of(x,y) :- child_of(x,z), child_of(z,y). - All variables (starting with capital letters) are universally quantified. The rule can be read For any X, Y and Z, if X is a child of Z and Z is a child of Y, then X is a grand child of Y. - Rules can be rephrased such that variables appearing only in the body of a rule are existentially quantfied. In this case, X is a grand child of Y, if there is some Z, of which X is a child, and is a child of Y. - A program may be regarded as a knowledge base, combining explicit knowledge of facts as well as implicit knowledge by means of rules. This knowledge may be queried by negative rules (no head). Notice that due to the negation, variables are read existentially. - Examples: Are there any parents of Alex (any X of which John is a parent)??- child_of(x,alex). Are there any A and B such that A is a grand parent of B (or B is a grand child of A)??- grand_child_of(a,b). Foundations of Logic and Constraint Programming 2
3 Prolog by Example child_of(john, ann). child_of(john, alex). child_of(bob, john). grand_child_of(x,y) :- child_of(x,z), child_of(z,y). - A Prolog engine is able to answer the queries (by implementing resolution on Horn clauses), finding all solutions and presenting them, one at a time.?- child_of(x, alex). X = john; no.?- grand_child_of(a,b). A = bob, B = ann ; A = bob, B = alex; no. - In practice, to program in Prolog, it is important to understand the options that Prolog engines assume, in applying resolution. - Informally, to search for all solutions, Prolog uses the query as an initial resolvent, and organises all the other resolvents in an execution tree. - Solutions, if any, are the success leafs of the tree (the other leafs are failed). Foundations of Logic and Constraint Programming 3
4 Prolog by Example child_of(john, ann). child_of(john, alex). child_of(bob, john). grand_child_of(x,y) :- child_of(x,z), child_of(z,y). - For example, query?- grand_child_of(a,b), expands into the execution tree grand_child_of(a,b) X/A, Y/B child_of(a,z), child_of(z,b) A/john Z/ann A/john Z/alex child_of(ann,b) child_of(alex,b) child_of(john,b) B/ann A/bob Z/john B/alex - Notice that Instances of the answers are obtained by composing the substitutions in a path to a successful leaf The tree is searched depth-first, left-to-right. Foundations of Logic and Constraint Programming 4
5 Prolog by Example: Family relationships - Let us assume some elements from the larger family tree. doug carol ann john mary vicky peter bob alex tess alice - The basic relationship that must be recorded is parent-child (the one kept in the ID cards and databases), modeled by the binary predicate child_of/2. fred child_of(john,doug). child_of(john,carol). child_of(mary,carol). child_of(tess,mary). child_of(fred,tess). child_of(peter,john). child_of(bob,john). child_of(alex,john). child_of(peter,ann). child_of(bob,ann). child_of(alex,ann). child_of(alice, peter). child_of(alice,vicky). Foundations of Logic and Constraint Programming 5
6 Prolog by Example: Family relationships - Other useful information can be introduced, such as gender (although usually implicit in the name but still this info is explicit in ID cards and passports). This is expressed by the unary predicate is_male/1 and is_female/1. is_male(doug). is_male(john). is_male(fred). is_male(peter). is_male(bob). is_male(alex). is_female(mary). is_female(carol). is_female(tess). is_female(ann). is_female(alice). is_female(vicky). vicky alice doug ann john peter bob alex carol mary tess fred - Once the basic relationships are established among the elements of the family, other family relationsships and predicates. For example, the relationship parent_of is the opposite of child_of: parent_of(x,y):- child_of(y,x). - The predicate mother is assigned to any female that is the parent of someone. mother_of(x,y):- parent_of(x,y), is_female(x). - A mother is the mother of someone. is_mother(x):- mother_of(x,_). Foundations of Logic and Constraint Programming 6
7 Prolog by Example: Repeated Answers - For any mother with many children, the predicate is_mother/1 may be deduced several times, once for each child. This leads to repeated answers to query?- is_mother(x). X= carol? ; X = carol? ; X = mary? ; X = tess? ; X = ann? ; is_mother(x) X = ann? ; X = ann? ; mother_of(x,y) X = vicky? ; no. parent_of(x,y), is_female(x). child_of(john,doug). child_of(john,carol). child_of(mary,carol). child_of(tess,mary). child_of(fred,tess). child_of(peter,john). child_of(bob,john). child_of(alex,john). child_of(peter,ann). child_of(bob,ann). child_of(alex,ann). child_of(alice, peter). child_of(alice,vicky). is_female(doug) X/john Y/doug child_of(y,x), is_female(x). X/john Y/carol is_female(carol) Foundations of Logic and Constraint Programming 7
8 Prolog by Example: Different Variables - Other indirect relationships may be derived from their definition, namely grand_child_of/2 sibling_of/2, brother_of/2, sister_of/2 uncle_of/2, aunt_of/2, great_uncle_of, great_aunt_of/2, cousin_of, second_cousin_of/2, third_cousin_of/2,... - Although most definitions are direct, some care must be taken. For example, siblings are children of a common parent sibling_of(x,y):- child_of(x,z), child_of(y,z). - This definition suffers from a quite common mistake: to assume that different variables should stand for different values. In the definition above a person is a sibling of him/herself! - Here is the correct definition, where the difference (\=) is made explicitely: sibling_of(x,y):- child_of(x,z), child_of(y,z). X \= Y. Foundations of Logic and Constraint Programming 8
9 Prolog by Example: Different Variables child_of(john,doug). child_of(john,carol). child_of(mary,carol). child_of(tess,mary). child_of(fred,tess). child_of(peter,john). child_of(bob,john). child_of(alex,john). child_of(peter,ann). child_of(bob,ann). child_of(alex,ann). child_of(alice, peter). child_of(alice,vicky). sibling_of(x,y):- child_of(x,z), child_of(y,z), X \= Y. sibling_of(x,y) vicky alice doug ann john peter bob alex carol mary tess fred X/john Z/doug child_of(x,z), child_of(y,z), X \= Y. X/john Z/carol child_of(y,doug), john\= Y child_of(y,carol), john\= Y Y/john john\= john Y/mary john\= mary Foundations of Logic and Constraint Programming 9
10 Prolog by Example: Non-termination - Care must also be taken to avoid definitions that, correct as they might be, eventually become circular, leading to non termination. - For example, the simetric property of the sibling_of relationship could, in principle, be explicitely specified, by the additional rule sibling_of(x,y):- sibling_of(y,x). - But this definition would lead, when X and Y are non-ground, to an infinite tree: sibling_of(x,y):- child_of(x,z), child_of(y,z), X \= Y. sibling_of(x,y):- sibling_of(y,x). child_of(x,z), child_of(y,z), X \= Y. sibling_of(x,y) sibling_of(y,x) sibling_of(x,y) sibling_of(y,x) sibling_of(x,y) Foundations of Logic and Constraint Programming 10
11 Prolog by Example: Peano Arithmetics - Logic has been used to formalise arithmetics, and a number of interesting (mostly theoretical) results where obtained from this effort (for example, the famous Gödel incompletness theorem). - The standard formalisation is due to Peano (end of 19th century), that proposed a simple set of axioms, for this purpose. - To begin with, integers are defined inductively: an integer is either 0 or the sucessor of another integer. - The basic algebraic operations can also be formalised, again inductively. For example the addition of two integers: Base clause: The sum of 0 and some integer M, is that integer. Inductive clause: The sum of the successor of an integer M and another integer N is the successor of the sum of the integers M and N. - Similar definitions can be used to define the operations of multiplication and potentiation. - Logic programming can thus be used to directly implement arithmetics (although in a very inefficient way). Foundations of Logic and Constraint Programming 11
12 Prolog by Example: Peano Arithmetics - The definition of integers is straighgtforward. Below the predicate int/1 is used to assign the property intehger, and the functor s/1 to denote the successor of an integer. int(0). % 0 is an integer int(s(m)):- int(m). % the successor of an integer is integer. - The addition follows directly the definition. sum(0,m,m). % The sum of 0 and any integer M is M sum(s(n),m,s(k)):- % The sum the successor of N and M is the sum(n,m,k). % successor of the sum of N and M. - The product, as a repeated sum, is modelled by means of addition. prod(0,m,0). % The product of 0 with any integer is 0. prod(s(n),m,p):- % The product of the successor of N and M is prod(n,m,k), % the sum of M with the product of M and N. sum(k,m,p). % i.e. (N+1)*M = N*M + M - And so is the power, as a repeated multiplication (the exponent is the first argument) pow(0,0, s(0)). % 0 raised to 0 is 0. pow(0,s(_),s(0)). % Integer M (>0) raised to 0 is 1 (i.e. S(0)). pow(s(n),m,p):- % Integer M raised to the successor of N pow(n,m,k), % is the product of M with M raised to N. prod(k,m,p). % i.e. M^(N+1) = M^N * M Foundations of Logic and Constraint Programming 12
13 Prolog by Example: Peano Arithmetics - It is interesting to note the functioning of Prolog, with these predicates. - First, the predicate integer can be used either to check whether an argument is an integer, either to generate integers.?- int(s(s(0))). yes?- int(x). X = 0? ; % X=0 X = s(0)? ; % X=1 X = s(s(0))? ; % X=2 X = s(s(s(0)))? % X=3?- int(s(s(x))). X = 0? ; % X = s(0)? ; - Notice in the last case, that the arguments of predicate int that are reported in the answers are usually denoted by 2, 3,... Foundations of Logic and Constraint Programming 13
14 Prolog by Example: Peano Arithmetics - The predicate sum performs as expected. Given two numbers to be summed, the predicate returns their sum. Let us sum 3 with 2?- sum(s(s(0)),s(s(s(0))),x). X = s(s(s(s(s(0)))))? ;no - The corresponding execution tree can be displayed sum(s(s(0)))),s(s(s(0))),x) sum(0,m,m). sum(s(n),m,s(k)):- sum(n,m,k). M1 / s(s(s(0))) N1 / s(0); X / s(k1) sum(s(0),s(s(s(0))),s(k1)) M2 / s(s(s(0))) N2 / 0 ; K1 / s(k2) sum(s(s(s(0))),0,s(k2)) K2 / s(s(s(0))) The result X is then obtained by composition of substitutions X/s(K1) but K1/s(K2)) so X/s(s(K2)) but K2/s(s(s(0))) so X/s(s(s(s(s(0))))) i.e. X = 5 Foundations of Logic and Constraint Programming 14
15 Prolog by Example: Peano Arithmetics - Logic programming is flexible. Predicate sum also defines subtraction! Given two numbers to be subtracted, the predicate also returns their difference. Let us subtract 2 from 5?- sum(s(s((0)),s(s(s(0))),x). X = s(s(s(s(s(0)))))? ;no sum(0,m,m). sum(s(n),m,s(k)):- sum(n,m,k). sum(s(s(0)),x,s(s(s(s(s(0)))))) M1 / X ; N1 / s(0) K1 / s(s(s(s(0)))) sum(s(0),x, s(s(s(s(0)))) M2 / X ; N2 / 0 K2 / s(s(s(0))) sum(0,x,s(s(s(s(s(0))))) X / s(s(s(0))) Foundations of Logic and Constraint Programming 15
16 Prolog by Example: Peano Arithmetics - The flexibility of logic programming allows that still the same definition enables to find all operands whose sum is 5.?- sum(y,s, sum(s(s(s((0)))). Y = s(s(s(s(s(0))))), X = 0? ; Y = s(s(s(s(0)))), X = s(0)? ; Y = s(s(s(0))), X = s(s(0))? ; Y = s(s(0)), X = s(s(s(0)))? ; Y = s(0), X = s(s(s(s(0))))? ; Y = 0, X = s(s(s(s(s(0)))))? ; no X / s(s(s(s(s(0))))) Y / 0 sum(y,x,s(s(s(s(s(0)))))) M1 / X ; Y / s(n1) K1 / s(s(s(s(0)))) sum(0,m,m). sum(s(n),m,s(k)):- sum(n,m,k). sum(n1,x,s(s(s(s(0))))) X / s(s(s(s(0)))) N1 / 0 M2 / X ; N1 / s(n2) K2 / s(s(s(0))) sum(n2,x,s(s(s(0)))) X / s(s(s(0))) N2 / 0 Foundations of Logic and Constraint Programming 16
17 Prolog by Example: Peano Arithmetics - The other predicates, for product and potentiation, behave similarly to the predicate for sum. However, if no solutions exist there might be termination problems, if the recursion is performed in the wrong argument. For example, there are no problems with 2 * X = 3 prod(s(s(0)),x,s(s(s(0)))) prod(s(0),x,k1), sum(x,k1,s(s(s(0)))) prod(0,x,k2), sum(x,k2,k1), sum(x,k1,s(s(s(0)))) sum(0,x,k1), sum(x,k1,s(s(s(0)))) X / M1, K1 / M1 ) sum(m1,m1,s(s(s(0)))) M1 / s(n2) sum(n2, s(n2), s(s(0))) N2 / s(n3) sum(n3, s(s(n3)), s(0)) N3 / s(n4) sum(n4, s(s(s(s(n4)), 0) prod(0,m,0). prod(s(n),m,p):- prod(n,m,k) sum(k,m,p). sum(0,m,m). sum(s(n),m,s(k)):- sum(n,m,k). Foundations of Logic and Constraint Programming 17
18 Prolog by Example: Peano Arithmetics - However, the same is not true for X * 2 = 3, where the unknown argument is the one used in the recursion. prod(0,m,0). prod(s(n),m,p):- prod(x,s(s(0)),s(s(s(0)))) prod(n,m,k) M1/s(s(0)), X /s(n1) sum(k,m,p). prod(n1,s(s(0)),k1), sum(n1,s(s(0)),s(s(s(0)))) sum(0,m,m). N1 / 0, K1 / 0 sum(s(n),m,s(k)):- sum(0,s(s(0)),s(s(s(0)))) sum(n,m,k). M2/s(s(0)) ; N1/s(N2), K1 / P2 prod(n2,s(s(0)),k2), sum(k2,s(s(0)),p2), sum(p2,s(s(0)),s(s(s(0)))) M3/s(s(0)) ; N2/s(N3), K2 / P3 prod(n3,s(s(0)),k3), sum(k3,s(s(0)),p3), sum(...), sum(...) M4/s(s(0)) ; N3/s(N4), K3 / P4 prod(n4,s(s(0)),k4), sum(k4,s(s(0)),p4), sum(...), sum(...), sum(...) - It is left as an exercise to check what types of calls do not terminate with the above definitions. Foundations of Logic and Constraint Programming 18
19 Prolog by Example: Peano Arithmetics - Although important from a theoretical viewpoint, Peano arithmetics is not very useful in practice due to the complexity of both the representation of numbers and the basic operations. - For example, the usual repretsentation of an integer N in the usual base 2 or 10 requires O(lg 2 N) or O(lg 10 N) bits. In contrast, Peano representation requires O(N) symbols (more precisely N s s + 2N parenthesis + 1 zero, which is significantly larger. - As to the sum operation, say N plus N, the usual method is proportional to the number of bits / digits i.e. it has complexity O(lg N). - In contrast, peano sum requires N calls to the sum definition, i.e. It has complexity O(N) sum(s(s(s(0))),x,p) sum(s(s(0)),x,p) sum(s(0),x,p) sum(0,x,p) sum(m,0,m). sum(s(n),m,s(k)):- sum(n,m,k). Foundations of Logic and Constraint Programming 19
20 List Processing in Prolog: Length - If Peano arithmetics is not very useful in practice, the same kind of definitions are widely applicable, namely in structures like lists. - Assuming the Peano representation of integers, the following definition of predicate p_lenght/2 highlights the correspondence between 0 and the empty list as well as between the s and the list functors p_length([],0). p_length([_ T],s(N)):- p_lenght(t,n). - Of course, if the usual arithmetics is used, the definition has to be adapted, such that the notion of successor is replaced by the usual +1 operation a_length([],0). a_length([_ T], M):- a_length(t,n), M is N+1. - There are however disadvantages in this formulation, namely non-termination. This is illustrated by the execution trees of both predicates to obtain lists of size 2. Foundations of Logic and Constraint Programming 20
21 List Processing in Prolog : Length - There are however disadvantages in this formulation, namely non-termination. This is illustrated by the execution trees of both predicates to obtain lists of size 2. - In the peano modelling, the goal is of course?- p_length(l,s(s(0))). and the execution tree is as follows p_length(l,s(s(0))) L/ [_ T1] p_length(t1,s(0))) L1/ [_ T2] p_length(t2,0) P_length([],0). P_length([_ T],s(N)):- p_lenght(t,n). T2/ [] Composing substitutions, the value of L is obtained T2 = [] T1 = [_ T2] = [_] L = [_ T1] = [_,_] Foundations of Logic and Constraint Programming 21
22 List Processing in Prolog : Length - With the modelling with standard arithmentics, the corresponding tree, for query?- a_length(l,2), is more complex a_length([],0). a_length([_ T],M):- a_lenght(t,n), M is N+1. a_length(l,2) a_length(t1,n1), 2 is N1+1 L/ [_ T1], M / 2 T1/ [], N1 / 0 2 is 0+1 T2/[], N2/0 N1 is 0+1, 2 is N1+1 T1/ [_ T2], M2 / N1 a_length(t2,n2), N1 is N2+1, 2 is N1+1 T2/ [_ T3], M3 / N2 a_length(t3,n3), N2 is N3+1,... 2 is 1+1 N1/1 - The correct answer is obtained as before, in the left part of the tree T2 = [] ; T1 = [_ T2] = [_]; L = [_ T1] = [_,_] - However, there is now a right part of the tree... Foundations of Logic and Constraint Programming 22
23 List Processing in Prolog : Length - However, the right part of the execution tree is infinite! a_length([],0). a_length([_ T],M):- a_lenght(t,n), M is N+1. a_length(t3,n3), N2 is N3+1,... T4/ [_ T3], M3 / N2 N3 is 0+1,..., 2 is N1+1 a_length(t4,n4), N3 is N4+1,... T4/ [_ T3], M3 / N2 N4 is 0+1,..., 2 is N1+1 a_length(t5,n5), N4 is N5+1,... T4/ [_ T3], M3 / N2 N5 is 0+1,..., 2 is N1+1 a_length(t6,n6), N5 is N6+1,... Foundations of Logic and Constraint Programming 23
24 List Processing in Prolog: Concatenation - A very common operation between lists is their concatenation. Predicate cat/3 below is true, when the list in the third argument is the concatenation of the lists in the first and second arguments. - As usual, the definition below relies on the inductive structure of the first list, and considers the cases where it is empty (the base clause) or not (the induction clause). cat([],l,l). cat([h T],L,[H R]):- cat(t,l,r). - It is interesting to notice in the execution tree, that concatenating a list with N 1 elements with a list with N 2 elements, requires N 1 calls to the recursive clause, for lists with sizes N 1, N 1-1, N 1-2,..., 2, 1. N 1 trivial failed calls to the base clause, for these lists (in fact, implementations of prolog indexing on the first argument do not make these calls). 1 successful call with an empty list as first argument. - The concatenation of a list requires thus N 1 +1 (non-trivial) calls, and presents thus a complexity of O(N), where N is the size of the first list argument. Foundations of Logic and Constraint Programming 24
25 List Processing in Prolog: Concatenation - From an algorithmic view point, this complexity is the one that can be expected for lists, maintained as simply linked lists, with a pointer to its head (first element). - This is in fact the case with Prolog, where lists are maintained in this form. However, a different form of representation, difference lists, allow the tail append to be a simple operation, as if lists were implemented with a pointer to their tail. - In any case, the declarativity of this definition allows the use of this cat/3 predicate either to concatenate two lists into a third one, or to remove a sublist (prefix or postfix) from a list.?- cat([1,2],[3,4,5],l). L = [1,2,3,4,5]; no.?- cat(l,[3,4,5],[1,2,3,4,5]). L = [1,2]; no.?- cat([1,2],l,[1,2,3,4,5]). L = [3,4,5]; no.?- cat(l1,l2,[1,2,3]). L1 = [], L2 = [1,2,3]; L1 = [1], L2 = [2,3]; L1 = [1,2], L2 = [3]; L1 = [1,2,3], L2 = []; no. cat([],l,l). cat([h T],L,[H R]):- cat(t,l,r). Foundations of Logic and Constraint Programming 25
26 List Processing in Prolog: Sublists - The declarativity of logic programming, makes it possible to reuse the definition of concatenation, to define other relations between a list and its (non-empty) sublists. - Prefix: List P is a (non-empty) prefix of list L if there is some other list X such that L is the concatenation of P and X (in Prolog, X may be declared as an anonimous list). prefix([h T],L):- cat([h T],_,L). - Posfix: List P is a (non-empty) postfix of list L if there is some other list X such that L is the concatenation of X and P (in Prolog, X may be declared as an anonimous list). posfix_of([h T],L):- cat(_,[h T],L). - Sublist: The sublist relation can be defined upon the prefix and posfix relations: list S is a (non-empty) sublist of L if there is a prefix P of list L, of which S is a posfix. sublist(s,l):- prefix(p,l), posfix(s,p). Foundations of Logic and Constraint Programming 26
27 List Processing in Prolog: Member and Insert - In addition to relationships bewteen lists, it is often important to consider relationships between lists and their members. - The most useful predicate, member/2, relates a list with any of its members member(x,[x _]). member(x,[_ T]):- member(x,t). - Another important predicate relates two lists, L1 and L2, with an element X. Given the declarativeness of logic programming this predicate can either be interpreted as Inserting X into L1 to obtain L2 Removing X from L2 to otain L1 - The definition is similar to that above, considering the cases where the insertion is done in the beginning or not of list L1. insert(x,l,[x L]). insert(x,[h T], [H R]):- insert(x,t,r). Foundations of Logic and Constraint Programming 27
28 List Processing in Prolog: Permutation and Reversion - Other interesting predicates relate a list with any of its permutations. As usual the definition considers two cases The (only) permutation of an emptry list is an empty list A permutation of a non-empty list is a permutation of its tail, to which the head is inserted. perm([],[]). perm([h T],L):- perm(t,p), insert(h,p,l). - A similar definition is used to relate a list with its reverse. The (only) reversion of an empty list is an empty list A reversion of a non-empty list is a reversion of its tail, to which the head is inserted at the end (this append at the end can be obtained by concatenation of the list with a list composed of the element to be appended) reverse([],[]). reverse([h T], L):- reverse(t, R), cat(r,[h], L). - Notice the non termination problems when the first argument is a variable. Why? Foundations of Logic and Constraint Programming 28
29 List Processing in Prolog : Permutation and Reversion - The reversion of a list is not very efficient. Analysing the execution tree (left as an exercise), the reversion of a list of size N requires One (non-trivial) call to revert a list (of length N-1) One call to append an element to the end of this list, which requires N non-trivial calls to predicate cat/3. - Hence, the complexity of this algorithm measured by the number of non-trivial calls, is 1 call to reverse and a call to cat for a list of length N (i.e. N+1 calls to cat) 1 call to reverse and a call to cat for a list of length N-1 (i.e. (N-1)+1 calls to cat)... 1 call to reverse and a call to cat for a list of length 1 (i.e. 1+1 calls to cat) 0 call to reverse and 1 call to cat for a list of length 0 (i.e. 0+1 calls to cat) - The number of calls is thus N (non-trivial) calls to predicate reverse [N+1]+ [(N-1)+1] = (N+1) (N+2) / 2 (non-trivial) calls to predicate cat - The complexity of the algorithm is then O(N 2 ) which is quite inefficient, since it is quite easy to get an algorithm to perform reversion of a list in O(N) steps. Foundations of Logic and Constraint Programming 29
30 List Processing in Prolog: Difference Lists - As seen before, concatenation of lists could be made more efficient if a pointer to the end of the list is maintained. This is the basic idea of the coding of lists as difference lists. - A difference list is a structure L-T where L and T are lists and T is the tail of L. - This structure represents a list whose elements are those belonging to L but not to T, (hence the name and the functor used). For example, the difference list [1,2,3,4,5,6]-[5,6] encodes list [1,2,3,4]. - The interesting case for processing is the case where T is a variable. In this case, appending to the end of the list requires processing T. - For example, assume list [1,2,3,4], encoded as [1,2,3,4 T]-T. Appending 5 to this list, corresponds to Obtaining a new tail T = [5 S] Subtracting L by S. - This is the declarative meaning of predicate td_app/3 td_app(x,l-t,l-s):- T = [X S]. which can be simplified with head unification td_app(x,l-[x S],L-S). Foundations of Logic and Constraint Programming 30
31 List Processing in Prolog: Difference Lists - The same technique can be used to concatenate two difference lists, L1-T1 and L2-T2, in to a third one L3-T3. - To exemplify, let us concatenate lists [1,2,3] to [4,5] resulting into [1,2,3,4,5], all encoded as difference lists [1,2,3 T1] - T1 + [4,5 T2]-T2 = [1,2,3,4,5 T3] T3 - By analysing this example, it is clear that We can make L1 = L3 if the substitution T1 = [4,5 T3] is imposed Since L2 = [4,5 T2], the above substitution is imposed when T2 = T3 and T1 = L2 - Hence predicate cat_diff/3, describes the concatenation of difference lists cat_diff(l1-t1,l2-t2,l3-t3):- L3 = L1, T3 = T2, L2 = T1 - By using head unification the concatenation becomes quite intuitive cat_diff(l1-t1,t1-t2,l1-t2). Foundations of Logic and Constraint Programming 31
32 List Processing in Prolog: Difference Lists - The concatenation of difference lists is thus performed through simple unification, instead of requiring the inefficient recursion of the usual lists. - This result can thus be used to reverse difference lists, by adapting the previous definition of reverse/2 (for standard lists) to the new encoding as difference lists (the special encoding of the empty difference list is exaplained in the next slide) rev_diff(l-t,l-t):- L == T. rev_diff([h L1]-T1, L2-T2):- rev_diff (L1-T1, Lx-Tx), cat_diff(lx-tx,[h T]-T,L2-T2). reverse([],[]). reverse([h T], L):- reverse(t, R), cat(r,[h], L). - The definition can be improved by head unification. Since the call to cat_diff/3 performs substitutions Lx = L2, Tx = [H T] and T = T2, such substitutions can be made directly, avoiding the explicit call to cat_diff/3 rev_diff(l-t,l-t):- L == T. rev_diff([h L1]-T1, L2-T):- rev_diff (L1-T1, T1-[H T]). Foundations of Logic and Constraint Programming 32
33 List Processing in Prolog: Difference Lists - In principle, the encoding of an empty difference list is L-L. As such the reversion of an empty difference list could be made with a clause such as rev_diff(l-l,l-l). rev_diff(l-t,l-t):- L = T - Hence, when this clause is tested to reverse a non-empty list, say rev_diff([1,2 Z]-Z, X-Y), the call should fail, since [1,2 Z]-Z does not encode an empty list (it encodes of course list [1,2]) and should not unify with L-L. - More precisely, it is not possible to unify L = [1,2 Z] and L = Z, because that would require Z = [1,2 Z], i.e. to substitute a variable, Z, by a term, [1,2 Z], where the variable occurs. - This occurs-check failure does not occur in most Prolog systems that do not implement it correctly (ending in an infinite loop X = f(x) = f(f(x)) = f(f(f(x))) =...). - For this reason, instead of checking if the two variable L-T are the same through unification (i.e. with predicate =/2 ), the clause tests this case with predicate ==/2, that only succeeds if the terms are already the same at the time of call. rev_diff(l-t,l-t):- L == T Foundations of Logic and Constraint Programming 33
34 List Processing in Prolog: Langford - The declarativity of Prolog allows simple programs to solve apparently complex problems. - The Langford(M,N) problem aims at finding a list of M*N elements, such that the integers 1 to M each appear N times, in such positions that between two occurrences of any J (in the range 1..M) are separated by J different elements. - The specification of the Langford(4,2) is quite obvious us when the sublist/2 predicate is used langford42(l):- L = [_,_,_,_,_,_,_,_], sublist([1,_,1], L), sublist([2,_,_,2], L), sublist([3,_,_,_,3], L), sublist([4,_,_,_,_,4], L). - Of course, such simple specification is only possible due to the flexibility of logic programming, namely the lack of fixed input-output arguments. Foundations of Logic and Constraint Programming 34
35 List Processing in Prolog: Zebra - A more challenging problem is the classic zebra puzzle: 1. There are five houses, each of a different color and inhabited by men of different nationalities, with different pets, drinks, and cigarettes. 2. The Englishman lives in the red house. 3. The Spaniard owns the dog. 4. Coffee is drunk in the green house. 5. The Ukrainian drinks tea. 6. The green house is immediately to the right of the ivory house. 7. The Old Gold smoker owns snails. 8. Kools are smoked in the yellow house. 9. Milk is drunk in the middle house. 10.The Norwegian lives in the first house on the left. 11.The man who smokes Chesterfields lives in the house next to the man with the fox. 12.Kools are smoked in the house next to the house where the horse is kept. 13.The Lucky Strike smoker drinks orange juice. 14.The Japanese smoke Parliaments. 15.The Norwegian lives next to the blue house. 16.NOW, who drinks water? And who owns the zebra? Foundations of Logic and Constraint Programming 35
36 List Processing in Prolog: Zebra - Again, this problem is solved with a very simple program, but requires slightly more involved data structures. Here is a possible solution A solution is a list of 5 entities, each composed of a house, a nationality, a pet, a drink and a cigarrette brand. These different components can be associated in a single term, h(h,n,p,d,c). In list L, an element A that is before another element B, encodes the fact that house H A is to the left of house H B. - Once this is done, the program has the following structure, where the constraints are still to be specified zebra(l):- L = [h(h1,n1,p1,d1,c1), h(h2,n2,p2,d2,c2), h(h3,n3,p3,d3,c3), h(h4,n4,p4,d4,c4), h(h5,n5,p5,d5,c5)],... constraints... Foundations of Logic and Constraint Programming 36
The Foundations: Logic and Proofs. Chapter 1, Part III: Proofs
The Foundations: Logic and Proofs Chapter 1, Part III: Proofs Rules of Inference Section 1.6 Section Summary Valid Arguments Inference Rules for Propositional Logic Using Rules of Inference to Build ArgumentsMore information
CHAPTER 7 GENERAL PROOF SYSTEMS 1 Introduction Proof systems are built to prove statements. They can be thought as an inference machine with special statements, called provable statements, or sometimesMore information
Predicate Logic. M.A.Galán, TDBA64, VT-03
Predicate Logic 1 Introduction There are certain arguments that seem to be perfectly logical, yet they cannot be specified by using propositional logic. All cats have tails. Tom is a cat. From these twoMore information
Artificial Intelligence
Artificial Intelligence ICS461 Fall 2010 1 Lecture #12B More Representations Outline Logics Rules Frames Nancy E. Reed firstname.lastname@example.com 2 Representation Agents deal with knowledge (data) Facts (believeMore information
Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay
Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture - 17 Shannon-Fano-Elias Coding and Introduction to Arithmetic CodingMore information
Lecture 4: Lists. Theory
Lecture 4: Lists Theory Introduce lists, an important recursive data structure often used in Prolog programming Define the member/2 predicate, a fundamental Prolog tool for manipulating lists IllustrateMore information
Predicate Calculus. There are certain arguments that seem to be perfectly logical, yet they cannot be expressed by using propositional calculus.
Predicate Calculus (Alternative names: predicate logic, first order logic, elementary logic, restricted predicate calculus, restricted functional calculus, relational calculus, theory of quantification,More information
Predicate Logic. For example, consider the following argument:
Predicate Logic The analysis of compound statements covers key aspects of human reasoning but does not capture many important, and common, instances of reasoning that are also logically valid. For example,More information
Full and Complete Binary Trees
Full and Complete Binary Trees Binary Tree Theorems 1 Here are two important types of binary trees. Note that the definitions, while similar, are logically independent. Definition: a binary tree T is fullMore information
CHAPTER 3. Methods of Proofs. 1. Logical Arguments and Formal Proofs
CHAPTER 3 Methods of Proofs 1. Logical Arguments and Formal Proofs 1.1. Basic Terminology. An axiom is a statement that is given to be true. A rule of inference is a logical rule that is used to deduceMore information
ML for the Working Programmer
ML for the Working Programmer 2nd edition Lawrence C. Paulson University of Cambridge CAMBRIDGE UNIVERSITY PRESS CONTENTS Preface to the Second Edition Preface xiii xv 1 Standard ML 1 Functional ProgrammingMore information
Borland C++ Compiler: Operators
Introduction Borland C++ Compiler: Operators An operator is a symbol that specifies which operation to perform in a statement or expression. An operand is one of the inputs of an operator. For example,More information
3. Mathematical Induction
3. MATHEMATICAL INDUCTION 83 3. Mathematical Induction 3.1. First Principle of Mathematical Induction. Let P (n) be a predicate with domain of discourse (over) the natural numbers N = {0, 1,,...}. If (1)More information
Relations: their uses in programming and computational specifications
PEPS Relations, 15 December 2008 1/27 Relations: their uses in programming and computational specifications Dale Miller INRIA - Saclay & LIX, Ecole Polytechnique 1. Logic and computation Outline 2. ComparingMore information
Programming Languages in Artificial Intelligence
Programming Languages in Artificial Intelligence Günter Neumann, German Research Center for Artificial Intelligence (LT Lab, DFKI) I. AI programming languages II. Functional programming III. FunctionalMore information
WHAT ARE MATHEMATICAL PROOFS AND WHY THEY ARE IMPORTANT? introduction Many students seem to have trouble with the notion of a mathematical proof. People that come to a course like Math 216, who certainlyMore information
Puzzler: An Automated Logic Puzzle Solver
Puzzler: An Automated Logic Puzzle Solver Aleksandar Milicevic, Joseph P. Near, and Rishabh Singh Massachusetts Institute of Technology (MIT) Abstract. Solving logic puzzles is a difficult problem, requiringMore information
[Refer Slide Time: 05:10]
Principles of Programming Languages Prof: S. Arun Kumar Department of Computer Science and Engineering Indian Institute of Technology Delhi Lecture no 7 Lecture Title: Syntactic Classes Welcome to lectureMore information
1.1 Logical Form and Logical Equivalence 1
Contents Chapter I The Logic of Compound Statements 1.1 Logical Form and Logical Equivalence 1 Identifying logical form; Statements; Logical connectives: not, and, and or; Translation to and from symbolicMore information
The following themes form the major topics of this chapter: The terms and concepts related to trees (Section 5.2).
CHAPTER 5 The Tree Data Model There are many situations in which information has a hierarchical or nested structure like that found in family trees or organization charts. The abstraction that models hierarchicalMore information
Theory of Computation Prof. Kamala Krithivasan Department of Computer Science and Engineering Indian Institute of Technology, Madras
Theory of Computation Prof. Kamala Krithivasan Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture No. # 31 Recursive Sets, Recursively Innumerable Sets, EncodingMore information
Lecture 8: Resolution theorem-proving
Comp24412 Symbolic AI Lecture 8: Resolution theorem-proving Ian Pratt-Hartmann Room KB2.38: email: firstname.lastname@example.com 2014 15 In the previous Lecture, we met SATCHMO, a first-order theorem-prover implementedMore information
Chapter 7: Functional Programming Languages
Chapter 7: Functional Programming Languages Aarne Ranta Slides for the book Implementing Programming Languages. An Introduction to Compilers and Interpreters, College Publications, 2012. Fun: a languageMore information
Algorithms and Data Structures
Algorithms and Data Structures Part 2: Data Structures PD Dr. rer. nat. habil. Ralf-Peter Mundani Computation in Engineering (CiE) Summer Term 2016 Overview general linked lists stacks queues trees 2 2More information
SJÄLVSTÄNDIGA ARBETEN I MATEMATIK MATEMATISKA INSTITUTIONEN, STOCKHOLMS UNIVERSITET Automated Theorem Proving av Tom Everitt 2010 - No 8 MATEMATISKA INSTITUTIONEN, STOCKHOLMS UNIVERSITET, 106 91 STOCKHOLMMore information
Automata and Formal Languages
Automata and Formal Languages Winter 2009-2010 Yacov Hel-Or 1 What this course is all about This course is about mathematical models of computation We ll study different machine models (finite automata,More information
12 Abstract Data Types
12 Abstract Data Types 12.1 Source: Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: Define the concept of an abstract data type (ADT).More information
Probability Using Dice
Using Dice One Page Overview By Robert B. Brown, The Ohio State University Topics: Levels:, Statistics Grades 5 8 Problem: What are the probabilities of rolling various sums with two dice? How can youMore information
Predicate Logic. Example: All men are mortal. Socrates is a man. Socrates is mortal.
Predicate Logic Example: All men are mortal. Socrates is a man. Socrates is mortal. Note: We need logic laws that work for statements involving quantities like some and all. In English, the predicate isMore information
Cassandra. References:
Cassandra References: Becker, Moritz; Sewell, Peter. Cassandra: Flexible Trust Management, Applied to Electronic Health Records. 2004. Li, Ninghui; Mitchell, John. Datalog with Constraints: A FoundationMore information
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com MathematicalMore information
a 11 x 1 + a 12 x 2 + + a 1n x n = b 1 a 21 x 1 + a 22 x 2 + + a 2n x n = b 2.
Chapter 1 LINEAR EQUATIONS 1.1 Introduction to linear equations A linear equation in n unknowns x 1, x,, x n is an equation of the form a 1 x 1 + a x + + a n x n = b, where a 1, a,..., a n, b are givenMore information
Analysis of Algorithms I: Binary Search Trees
Analysis of Algorithms I: Binary Search Trees Xi Chen Columbia University Hash table: A data structure that maintains a subset of keys from a universe set U = {0, 1,..., p 1} and supports all three dictionaryMore information
Mathematics for Computer Science/Software Engineering. Notes for the course MSM1F3 Dr. R. A. Wilson
Mathematics for Computer Science/Software Engineering Notes for the course MSM1F3 Dr. R. A. Wilson October 1996 Chapter 1 Logic Lecture no. 1. We introduce the concept of a proposition, which is a statementMore information
CST.98.5.1 COMPUTER SCIENCE TRIPOS Part IB Wednesday 3 June 1998 1.30 to 4.30 Paper 5 Answer five questions. No more than two questions from any one section are to be answered. Submit the answers in fiveMore information
Introduction to Programming (in C++) Data types and visibility. Jordi Cortadella, Ricard Gavaldà, Fernando Orejas Dept. Computer Science, UPC
Introduction to Programming (in C++) Data types and visibility Jordi Cortadella, Ricard Gavaldà, Fernando Orejas Dept. Computer Science, UPC Outline Data types Type conversion Visibility Introduction toMore information
Software Engineering
Software Engineering Lecture 04: The B Specification Method Peter Thiemann University of Freiburg, Germany SS 2013 Peter Thiemann (Univ. Freiburg) Software Engineering SWT 1 / 50 The B specification methodMore information
Jieh Hsiang Department of Computer Science State University of New York Stony brook, NY 11794
ASSOCIATIVE-COMMUTATIVE REWRITING* Nachum Dershowitz University of Illinois Urbana, IL 61801 N. Alan Josephson University of Illinois Urbana, IL 01801 Jieh Hsiang State University of New York Stony brook,More information
Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 2
CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 2 Proofs Intuitively, the concept of proof should already be familiar We all like to assert things, and few of usMore information
Notes on Factoring. MA 206 Kurt Bryan
The General Approach Notes on Factoring MA 26 Kurt Bryan Suppose I hand you n, a 2 digit integer and tell you that n is composite, with smallest prime factor around 5 digits. Finding a nontrivial factorMore information
University of Ostrava. Reasoning in Description Logic with Semantic Tableau Binary Trees
University of Ostrava Institute for Research and Applications of Fuzzy Modeling Reasoning in Description Logic with Semantic Tableau Binary Trees Alena Lukasová Research report No. 63 2005 Submitted/toMore information
RN-coding of Numbers: New Insights and Some Applications
RN-coding of Numbers: New Insights and Some Applications Peter Kornerup Dept. of Mathematics and Computer Science SDU, Odense, Denmark & Jean-Michel Muller LIP/Arénaire (CRNS-ENS Lyon-INRIA-UCBL) Lyon,More information
Prolog A Tutorial Introduction James Lu Jerud J. Mead
Prolog A Tutorial Introduction James Lu Jerud J. Mead Computer Science Department Bucknell University Lewisburg, PA 17387 1 Contents 1 Introduction 1 2 Easing into Prolog 2 2.1 Logic Programming.........................................More information
Parametric Domain-theoretic models of Linear Abadi & Plotkin Logic
Parametric Domain-theoretic models of Linear Abadi & Plotkin Logic Lars Birkedal Rasmus Ejlers Møgelberg Rasmus Lerchedahl Petersen IT University Technical Report Series TR-00-7 ISSN 600 600 February 00More information
An Innocent Investigation
An Innocent Investigation D. Joyce, Clark University January 2006 The beginning. Have you ever wondered why every number is either even or odd? I don t mean to ask if you ever wondered whether every numberMore information
Chapter 7. Functions and onto. 7.1 Functions
Chapter 7 Functions and onto This chapter covers functions, including function composition and what it means for a function to be onto. In the process, we ll see what happens when two dissimilar quantifiersMore information
Today. Binary addition Representing negative numbers. Andrew H. Fagg: Embedded Real- Time Systems: Binary Arithmetic
Today Binary addition Representing negative numbers 2 Binary Addition Consider the following binary numbers: 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 How do we add these numbers? 3 Binary Addition 0 0 1 0 0 1 1More information
A first step towards modeling semistructured data in hybrid multimodal logic
A first step towards modeling semistructured data in hybrid multimodal logic Nicole Bidoit * Serenella Cerrito ** Virginie Thion * * LRI UMR CNRS 8623, Université Paris 11, Centre d Orsay. ** LaMI UMRMore information
8 Divisibility and prime numbers
8 Divisibility and prime numbers 8.1 Divisibility In this short section we extend the concept of a multiple from the natural numbers to the integers. We also summarize several other terms that expressMore information
Logic in general. Inference rules and theorem proving
Logical Agents Knowledge-based agents Logic in general Propositional logic Inference rules and theorem proving First order logic Knowledge-based agents Inference engine Knowledge base Domain-independentMore information
Compiler Design. Type Checking
Compiler Design Type Checking Static Checking Token Stream Parser Abstract Syntax Tree Static Checker Decorated Abstract Syntax Tree Intermediate Code Generator Intermediate Code Static (Semantic) ChecksMore information
DATA STRUCTURES USING C QUESTION BANK UNIT I 1. Define data. 2. Define Entity. 3. Define information. 4. Define Array. 5. Define data structure. 6. Give any two applications of data structures. 7. GiveMore information
The Zebra Puzzle. 1 Introduction. Carlo Tomasi Computer Science Duke University
The Puzzle Carlo Tomasi Computer Science Duke University 1 Introduction In the class textbook, the puzzle is offered as an exercise for Section 1.1 on logic (Exercise 61, page 20). Here is the puzzle:More information
PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical and Mathematical Sciences 2012 1 p. 43 48 ON FUNCTIONAL SYMBOL-FREE LOGIC PROGRAMS I nf or m at i cs L. A. HAYKAZYAN * Chair of Programming and InformationMore information
2. Methods of Proof Types of Proofs. Suppose we wish to prove an implication p q. Here are some strategies we have available to try.
2. METHODS OF PROOF 69 2. Methods of Proof 2.1. Types of Proofs. Suppose we wish to prove an implication p q. Here are some strategies we have available to try. Trivial Proof: If we know q is true thenMore information
Data Structure with C
Subject: Data Structure with C Topic : Tree Tree A tree is a set of nodes that either:is empty or has a designated node, called the root, from which hierarchically descend zero or more subtrees, whichMore information
BEGINNING ALGEBRA The Nursing Department of Labouré College requested the Department of Academic Planning and Support Services to help with mathematics preparatory materials for its Bachelor of ScienceMore information
Some facts about polynomials modulo m (Full proof of the Fingerprinting Theorem)
Some facts about polynomials modulo m (Full proof of the Fingerprinting Theorem) In order to understand the details of the Fingerprinting Theorem on fingerprints of different texts from Chapter 19 of theMore information
Logic Programming using Prolog an Introductory Exercise
Logic Programming using Prolog an Introductory Exercise Brandon Bennett The purpose of this exercise is for you to see some examples of the Prolog logic programming language in action. Prolog is very differentMore information
Notes from Week 1: Algorithms for sequential prediction
CS 683 Learning, Games, and Electronic Markets Spring 2007 Notes from Week 1: Algorithms for sequential prediction Instructor: Robert Kleinberg 22-26 Jan 2007 1 Introduction In this course we will be lookingMore information
Embedded Systems. Review of ANSI C Topics. A Review of ANSI C and Considerations for Embedded C Programming. Basic features of C
Embedded Systems A Review of ANSI C and Considerations for Embedded C Programming Dr. Jeff Jackson Lecture 2-1 Review of ANSI C Topics Basic features of C C fundamentals Basic data types Expressions SelectionMore information
7.1 Our Current Model
Chapter 7 The Stack In this chapter we examine what is arguably the most important abstract data type in computer science, the stack. We will see that the stack ADT and its implementation are very simple.More information
Chapter II. Controlling Cars on a Bridge
Chapter II. Controlling Cars on a Bridge 1 Introduction The intent of this chapter is to introduce a complete example of a small system development. During this development, you will be made aware of theMore information
Solution of Linear Systems
Chapter 3 Solution of Linear Systems In this chapter we study algorithms for possibly the most commonly occurring problem in scientific computing, the solution of linear systems of equations. We startMore information
CHAPTER II THE LIMIT OF A SEQUENCE OF NUMBERS DEFINITION OF THE NUMBER e.
CHAPTER II THE LIMIT OF A SEQUENCE OF NUMBERS DEFINITION OF THE NUMBER e. This chapter contains the beginnings of the most important, and probably the most subtle, notion in mathematical analysis, i.e.,More information
Levent EREN firstname.lastname@example.com A-306 Office Phone:488-9882 INTRODUCTION TO DIGITAL LOGIC
Levent EREN firstname.lastname@example.com A-306 Office Phone:488-9882 1 Number Systems Representation Positive radix, positional number systems A number with radix r is represented by a string of digits: A nMore information
Scalable Automated Symbolic Analysis of Administrative Role-Based Access Control Policies by SMT solving
Scalable Automated Symbolic Analysis of Administrative Role-Based Access Control Policies by SMT solving Alessandro Armando 1,2 and Silvio Ranise 2, 1 DIST, Università degli Studi di Genova, Italia 2 SecurityMore information
Elementary Number Theory and Methods of Proof. CSE 215, Foundations of Computer Science Stony Brook University http://www.cs.stonybrook.
Elementary Number Theory and Methods of Proof CSE 215, Foundations of Computer Science Stony Brook University http://www.cs.stonybrook.edu/~cse215 1 Number theory Properties: 2 Properties of integers (wholeMore information
Aikaterini Marazopoulou
Imperial College London Department of Computing Tableau Compiled Labelled Deductive Systems with an application to Description Logics by Aikaterini Marazopoulou Submitted in partial fulfilment of the requirementsMore information
each college c i C has a capacity q i - the maximum number of students it will admit
n colleges in a set C, m applicants in a set A, where m is much larger than n. each college c i C has a capacity q i - the maximum number of students it will admit each college c i has a strict order iMore information
µz An Efficient Engine for Fixed points with Constraints
µz An Efficient Engine for Fixed points with Constraints Kryštof Hoder, Nikolaj Bjørner, and Leonardo de Moura Manchester University and Microsoft Research Abstract. The µz tool is a scalable, efficientMore information
Relational Databases
Relational Databases Jan Chomicki University at Buffalo Jan Chomicki () Relational databases 1 / 18 Relational data model Domain domain: predefined set of atomic values: integers, strings,... every attributeMore information
3.6. The factor theorem
3.6. The factor theorem Example 1. At the right we have drawn the graph of the polynomial y = x 4 9x 3 + 8x 36x + 16. Your problem is to write the polynomial in factored form. Does the geometry of theMore information
The Set Data Model CHAPTER 7. 7.1 What This Chapter Is About
CHAPTER 7 The Set Data Model The set is the most fundamental data model of mathematics. Every concept in mathematics, from trees to real numbers, is expressible as a special kind of set. In this book,More information
Informatica e Sistemi in Tempo Reale
Informatica e Sistemi in Tempo Reale Introduction to C programming Giuseppe Lipari http://retis.sssup.it/~lipari Scuola Superiore Sant Anna Pisa October 25, 2010 G. Lipari (Scuola Superiore Sant Anna)More information
So let us begin our quest to find the holy grail of real analysis.
1 Section 5.2 The Complete Ordered Field: Purpose of Section We present an axiomatic description of the real numbers as a complete ordered field. The axioms which describe the arithmetic of the real numbersMore information
Foundations of mathematics
Foundations of mathematics 1. First foundations of mathematics 1.1. Introduction to the foundations of mathematics Mathematics, theories and foundations Sylvain Poirier http://settheory.net/ MathematicsMore information
Integer Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions
Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.More information
Python Lists and Loops
WEEK THREE Python Lists and Loops You ve made it to Week 3, well done! Most programs need to keep track of a list (or collection) of things (e.g. names) at one time or another, and this week we ll showMore information
Copyright 2012 MECS I.J.Information Technology and Computer Science, 2012, 1, 50-63
I.J. Information Technology and Computer Science, 2012, 1, 50-63 Published Online February 2012 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijitcs.2012.01.07 Using Logic Programming to RepresentMore information
MATH10212 Linear Algebra. Systems of Linear Equations. Definition. An n-dimensional vector is a row or a column of n numbers (or letters): a 1.
MATH10212 Linear Algebra Textbook: D. Poole, Linear Algebra: A Modern Introduction. Thompson, 2006. ISBN 0-534-40596-7. Systems of Linear Equations Definition. An n-dimensional vector is a row or a columnMore information
A set is a Many that allows itself to be thought of as a One. (Georg Cantor)
Chapter 4 Set Theory A set is a Many that allows itself to be thought of as a One. (Georg Cantor) In the previous chapters, we have often encountered sets, for example, prime numbers form a set, domainsMore information
MODULAR ARITHMETIC. a smallest member. It is equivalent to the Principle of Mathematical Induction.
MODULAR ARITHMETIC 1 Working With Integers The usual arithmetic operations of addition, subtraction and multiplication can be performed on integers, and the result is always another integer Division, onMore information
Measuring the Performance of an Agent
25 Measuring the Performance of an Agent The rational agent that we are aiming at should be successful in the task it is performing To assess the success we need to have a performance measure What is rationalMore information
2. Compressing data to reduce the amount of transmitted data (e.g., to save money).
Presentation Layer The presentation layer is concerned with preserving the meaning of information sent across a network. The presentation layer may represent (encode) the data in various ways (e.g., dataMore information
15-251: Great Theoretical Ideas in Computer Science Anupam Gupta Notes on Combinatorial Games (draft!!) January 29, 2012
15-251: Great Theoretical Ideas in Computer Science Anupam Gupta Notes on Combinatorial Games (draft!!) January 29, 2012 1 A Take-Away Game Consider the following game: there are 21 chips on the table.More information
Symbol Tables. Introduction
Symbol Tables Introduction A compiler needs to collect and use information about the names appearing in the source program. This information is entered into a data structure called a symbol table. TheMore information
We can express this in decimal notation (in contrast to the underline notation we have been using) as follows: 9081 + 900b + 90c = 9001 + 100c + 10b
In this session, we ll learn how to solve problems related to place value. This is one of the fundamental concepts in arithmetic, something every elementary and middle school mathematics teacher shouldMore information
Finite Automata and Formal Languages
Finite Automata and Formal Languages TMV026/DIT321 LP4 2011 Lecture 14 May 19th 2011 Overview of today s lecture: Turing Machines Push-down Automata Overview of the Course Undecidable and Intractable ProblemsMore information
Chapter 15 Functional Programming Languages
Chapter 15 Functional Programming Languages Introduction - The design of the imperative languages is based directly on the von Neumann architecture Efficiency (at least at first) is the primary concern,More information
Testing LTL Formula Translation into Büchi Automata
Testing LTL Formula Translation into Büchi Automata Heikki Tauriainen and Keijo Heljanko Helsinki University of Technology, Laboratory for Theoretical Computer Science, P. O. Box 5400, FIN-02015 HUT, FinlandMore information
Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test
Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are importantMore information
6 3 4 9 = 6 10 + 3 10 + 4 10 + 9 10
Lesson The Binary Number System. Why Binary? The number system that you are familiar with, that you use every day, is the decimal number system, also commonly referred to as the base- system. When youMore information
Generalized Modus Ponens
Generalized Modus Ponens This rule allows us to derive an implication... True p 1 and... p i and... p n p 1... p i-1 and p i+1... p n implies p i implies q implies q allows: a 1 and... a i and... a n impliesMore information
Class Notes CS 3137. 1 Creating and Using a Huffman Code. Ref: Weiss, page 433
Class Notes CS 3137 1 Creating and Using a Huffman Code. Ref: Weiss, page 433 1. FIXED LENGTH CODES: Codes are used to transmit characters over data links. You are probably aware of the ASCII code, a fixed-lengthMore information
(IALC, Chapters 8 and 9) Introduction to Turing s life, Turing machines, universal machines, unsolvable problems.
3130CIT: Theory of Computation Turing machines and undecidability (IALC, Chapters 8 and 9) Introduction to Turing s life, Turing machines, universal machines, unsolvable problems. An undecidable problemMore information
XML with Incomplete Information
XML with Incomplete Information Pablo Barceló Leonid Libkin Antonella Poggi Cristina Sirangelo Abstract We study models of incomplete information for XML, their computational properties, and query answering.More information
2. The Language of First-order Logic
2. The Language of First-order Logic KR & R Brachman & Levesque 2005 17 Declarative language Before building system before there can be learning, reasoning, planning, explanation... need to be able toMore information
Introduction to Logic in Computer Science: Autumn 2006
Introduction to Logic in Computer Science: Autumn 2006 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss 1 Plan for Today Now that we have a basic understandingMore information
This asserts two sets are equal iff they have the same elements, that is, a set is determined by its elements.
3. Axioms of Set theory Before presenting the axioms of set theory, we first make a few basic comments about the relevant first order logic. We will give a somewhat more detailed discussion later, butMore information


text:
Get an overview of this hotel4-star Lisbon hotel in Lisbon City Center, walk to Santa Justa Elevator
Collecting Nectar Points
Special Offer: Book by 2 August 2017 and collect double Nectar points!
Simply enter your Nectar card number when you check out. Your points will be credited 35 days after you return from your trip.
*Terms and conditions apply.
Popular property highlights
Located in Lisbon City Center, this hotel is within a 5-minute walk of Fernando Pessoa Statue, Santa Justa Elevator, and Rossio Square. Castle of Sao Jorge and Lisbon Cathedral are also within 1 mi (2 km).
Hotel Features
Along with a restaurant, this smoke-free hotel has a snack bar/deli and concierge services. Free WiFi in public areas and free self parking are also provided. Additionally, dry cleaning, a 24-hour front desk, and free newspapers are onsite.
Room Amenities
All 45 soundproofed rooms feature free WiFi and minibars. Comforts include premium bedding and pillow menus, and guests will also appreciate thoughtful touches like bathrobes and slippers.Information missing or incorrect? Tell us!Opens in a new window
Lisboa Carmo Hotel
Hotel Amenities
Hotel Amenities
The hotel offers a restaurant and a snack bar/deli. Public areas are equipped with complimentary wireless Internet access. This Lisbon hotel also offers multilingual staff, concierge services, and complimentary newspapers in the lobby. Onsite self parking is complimentary.
Lisboa Carmo Hotel is a smoke-free property.
- Snack bar/deli
- Breakfast available (surcharge)
- Elevator/lift
- Restaurant
- Luggage storage
- Smoke-free property
- Free WiFi
- 24-hour front desk
- Dry cleaning/laundry service
- Multilingual staff
- Total number of rooms - 45
- Number of floors - 5
- Free newspapers in lobby
- Concierge services
- Safe-deposit box at front desk
- Free self parking
- Number of buildings/towers - 1
Family Friendly Amenities
- Free Wi-Fi
- Soundproofed rooms
- Snack bar/deli
- Cribs/infant beds (complimentary)
Available in all rooms: Free WiFi
Available in some public areas: Free WiFi
Free self parking
Room Amenities
- Cable TV service
- Free WiFi
- Dial-up Internet access (surcharge)
- Pillow menu
- Premium TV channels
- Rainfall showerhead
- Connecting/adjoining rooms available
- Bathrobes
- Free toiletries
- Hair dryer
- In-room safe
- Desk
- In-room climate control (air conditioning)
- Premium bedding
- Soundproofed rooms
- Room service (limited hours)
- Minibar
- Daily housekeeping
- Blackout drapes/curtains
- Slippers
- Air conditioning
- Phone
- Free bottled water
- Private bathroom
- Shower/tub combination
- Free cribs/infant beds
Where to Eat
Buffet breakfasts are available for a surcharge and are served each morning between 7:30 AM and 10:30 AM.
Maria do Carmo - This restaurant specializes in Portuguese cuisine and serves breakfast, lunch, dinner, and light fare. Guests can enjoy drinks at the bar.
Room service (during limited hours) is available.
If you have requests for specific accessibility needs, please note them at check-out when you book your room.
- Accessible bathroom
- In-room accessibility
- Roll-in shower
Hotel Policies
Check-in time starts at 3 PM
Check-in time ends at midnight
Special check-in instructions:
Check-out time is noon
Payment types
Children and extra beds
- Children are welcome.
- Kids stay free! One child 12 years old or younger stays free when using existing bedding.
- Rollaway/extra beds are available for EUR 50.0 per night.
- Free cribs (infant beds)!
- Pets not allowed
You need to know
Extra-person charges may apply and vary depending on property policy.
Government-issued photo identification and a credit card or cash deposit are required at check-in for incidental charges.
Special requests are subject to availability upon check-in and may incur additional charges. Special requests cannot be guaranteed.
- A tax is imposed by the city: EUR 1 per person, per night, up to 7 nights. This tax does not apply to children under 13 years of age.
Optional extras
- Fee for buffet breakfast: EUR 12 per person (approximately)
- Rollaway bed fee: EUR 50.0 per night
Hotel Name
- Lisboa Carmo
- Lisboa Carmo Hotel
- Lisboa Carmo Hotel Lisbon
- Lisboa Carmo Lisbon
We should mention
One child 12 years old or younger stays free when occupying the parent or guardian's room, using existing bedding. Only registered guests are allowed in the guestrooms. The property has connecting/adjoining rooms, which are subject to availability and can be requested by contacting the property using the number on the booking confirmation.

subset: commoncrawl


text:
Four years ago, it outraged the families of those who died in the Air-India bombing disaster.
The children of Inderjit Singh Reyat were put on the payroll of his publicly funded legal defence team. The head of the legal team, Vancouver lawyer David Martin, submitted bills to the government to pay the children more than $10,000 a month for minimal work.
Yesterday, the Law Society of British Columbia suspended Mr. Martin for six months and required him to pay $35,000 for the cost of his disciplinary hearing.
Mr. Martin, who has practised law since 1979, is widely respected in B.C. legal circles for his professionalism, intellectual capacity and dedication to the practice of law. But the law society previously found the children's billings were fraudulent and Mr. Martin was guilty of professional misconduct for the "blatant and cavalier disregard" of his professional duties.
In considering the gravity of Mr. Martin's conduct, the three-member law society panel noted yesterday that Mr. Martin, after being briefed about the major problem with the children's accounts, said he didn't understand what the big fuss was about, as the amount of the Reyat accounts were 2 or 3 per cent of the overall monthly billings to defend Mr. Reyat.
"There was silence and then [lawyer Letitia]Sears said: because it's public funds, David," according to the agreed statement of facts.
The panel noted the comments of another member of the defence team, Todd Ducharme, when Mr. Martin floated the idea of also putting Mr. Reyat's wife on the government-funded, defence-team payroll.
"You don't pay your client for the privilege of representing them," Mr. Ducharme was reported to have said.
Mr. Martin's lawyer Josiah Wood argued that Mr. Martin was handling several cases at the same time and did not pay close attention to the billings submitted by the children and passed on to the government. If Mr. Martin did not have time to do a good job, he should not have taken the case, the panel concluded.
Mr. Reyat pleaded guilty in 2003 to collecting items used in a bomb that exploded aboard an Air-India flight from Toronto to London, killing 329 people.Report Typo/Error


text:
We use cookies to ensure that you have the best experience on our website. If you continue browsing, we'll assume that you are happy to receive all our cookies. You can change your cookie settings at any time.
Find out more
FREE DELIVERY until 31 MAY Ts&Cs Apply
1. The sale runs from 29 Mar 2017 to 19 Apr 2017, 3pm.
2. This offer is only valid for orders placed online.
3. This offer applies to selected items only.
4. The updated discounted price is shown on the product page.
5. Offer excludes unwrapped and bridal.
6. Oxfam offers a standard UK delivery charge of £3.95 on all orders containing donated products sent by Royal Mail, with the exception of wedding dresses and other high-value or bulky items, which incur a mandatory courier charge.
7. Oxfam reserves the right to end this promotion at any time.
You are here:
Share this product with your friends and family!
Published by the Genealogical Publishing Company, this is the 1967 reprint of Rev. Patrick Woulfe's Irish Names and Surnames, collected and edited with explanatory and historical notes.Good condition hardback on green boards with gilt titles to the spine. Some shelf wear and scuffing to the boards. The book is ex-reference library, and bears the associated markings and stamps.
Delivery FAQs
within 21 days.
Returns policy
Published by the Genealogical Publishing Company, this is the 1967 reprint of Rev. Patrick Woulfe's Irish Names and Surnames, collected and edited with explanatory and historical notes.Good condition hardback on green boards with gilt titles to the spine. Some shelf wear and scuffing to the boards. The book is ex-reference library, and bears the associated markings and stamps.
This item will be dispatched to UK addresses via second class post within 2 working days of receipt of your order. Standard UK delivery is £3.95 per order , so you're only charged once no matter how many items you have in your basket. Any additional courier charges will be applied at checkout as they vary depending on delivery address.
You can find out more about delivery and returns in our help section.
We offer a no quibble returns policy as follows:
Wedding dresses: 14 days
Overseas returns: 31 days
Everything else: 21 days
This item is also available for international delivery by airmail, carrying a mandatory delivery charge of:
Europe: £6.50
Outside Europe: £11.50
Wonder how this unique item ended up online?
Most of the second-hand items you see online have been donated, by supporters like you, to our high street stores. Each item is then priced, photographed and listed on this site by our amazing team of volunteers from across the country.
After you have bought your item, our team of volunteers package and dispatch it from the Shop straight to you or your chosen recipient.
All profits from the sales of our goods go towards funding Oxfam's work around the world. We rely on your donations to sell online so please keep the cycle of goodness going!
To find out more about volunteering with Oxfam, please visit our how to volunteer page.
Newport Books & Music is situated in the picturesque market square at the heart of the Isle of Wight's principal shopping centre, conventiently placed for public transport and parking. We stock a wide range of high quality used books and music, both vintage and modern, along with Oxfam's popular fair-trade gift products and an exclusive selection of work produced by local artists.
Oxfam is the UK's largest second hand bookseller. Oxfam bookshops offer a wider selection of books than most shops, from modern fiction and leisure interest to more specialist subjects, classics, and rare or collectable books. We also sell a good selection of attractive greetings cards. Come and browse!
View Shop
What we do
Get involved
Make a donation
© 2015. Oxfam is a registered charity in England and Wales (no 202918) and Scotland (SC039042).
Oxfam GB is a member of Oxfam International.
support oxfam


text:
Secretary Girl Dress Up
How to play
Secretary Girl Dress Up
Johanna works as a secretary at a big business company and she has to look impeccable at the office. Important people come here to discuss business with her boss and Johanna is the one who has to welcome them, so she should make a good impression to them. Her wardrobe is full of elegant office clothes and accessories and she always looks perfect at work. Help Johanna prepare for a new day in this cool game, check out her clothes and dress her up with the outfit you like best for a new working day. Don't forget she also needs some accessories and an elegant hairstyle. Enjoy!


text:
Complete non-selective broad-spectrum post-emergence herbicide for crop and non-crop, industrial, turf and ornamental and farmsteads.
Product Type: Consumer
Use Sites: pasture grasses, forage legumes, rangelands, crops, roundup ready, industrial, turf, ornamental, vegetables, gardens
Effective Against: annual weeds, perennial weeds, trees, vines, shrubs
Active Ingredients: Glyphosate 41%
States Registered: AL, AR, AZ, CA, CO, CT, DC, DE, FL, GA, HI, IA, ID, IL, IN, KS, KY, LA, MA, MD, ME, MI, MN, MO, MS, MT, NC, ND, NE, NH, NJ, NM, NV, NY, OH, OK, OR, PA, RI, SC, SD, TN, TX, UT, VA, VT, WA, WI, WV, WY
The story of Control Solutions, now a partner with ADAMA Consumer & Professional Solutions, began in 1958 when the Boyd family purchased a small Pasadena, Texas pest control company. Control Solutions continued as a family owned business and built on to the commitment of serving the professional pest control and retail markets after the Ford's sale to Roussel. Since that time, CSI has added product lines for the Industrial, Lawn and Garden, Animal Health and Biocide markets, and is working with 80 + distributors serving those markets. Control Solutions maintains relationships with chemical manufacturers worldwide and maintains a ready supply of products in numerous distribution warehouses across the U.S. Today our partnership with ADAMA (www.adama.com) multiplies Control Solutions' agility in continuously adding new products to meet the needs of professionals and homeowners. The one constant since the beginning in 1958 is our mission focus: to seek out and distribute effective and economical solutions for our customers.
Copyright © 2017 NRS World


text:
The Kennel Club would like to congratulate the Field Trials Team GB, who recently competed for the first time at the FCI World Championship Practical Hunting for Pointers and Setters and the St. Hubert Championship held in Niš, Serbia, thanks to the support of the Kennel Club.
This was the 37thWorld Championship, with 29 teams competing from countries including Russia, Turkey, Iceland, USA and Brazil. Field Trials Team GB's Rob Gould came joint 6thoverall in the Continental Pointing Breeds and Maddy Raynor was joint 15thposition in the British Pointing Breeds during the St. Hubert FCI World Championship.
The FCI World Championship took place on Saturday 24 and Monday 26 October, with the St. Hubert Championship, which included a Spaniel Trial and three classes for men and two for ladies, in between.
The Field Trials Team GB captain was Meryl Asbury, and the team vet was Rob Gould. The full team was as follows:
World Championship Pointers and Setters
World Championship Continentals
St Hubert (Mens)
St Hubert (Womens)
St Hubert (Spaniels)
Handlers had to make their way through maize, chillies, wheat, stubble, plough and weed and, under FCI Rules, ran for 15 minutes.
On the first day, Rob Gould with Wamilanghaar Djynn gained a Very Good, being awarded 4 points towards the team and Maddy Raynor with Bownard Carrabullawn of Wiscombe gained a Good achieving 2 points.
On the second day, the groups split up for the St Hubert competition. During this competition they are judged as a hunter and 70 per cent of the marks go on how the hunter conducts him or herself, and 30 per cent go to the dog. The pair are given a piece of ground and hunt for 20 minutes.
On the third day, Rob Gould with Wamilanghaar Djynn gained another Very Good, being awarded 4 points in the World Championship again. This made him joint 6thoverall in the Continental Pointing Breeds, with Maddy Raynor finishing joint 15thposition in the British Pointing Breeds.
Meryl Asbury, Field Trials Team GB Captain said: "This was the first time we had competed in Europe under FCI Rules with world class competition and Team GB did very well. Our dogs held their own in terms of pace, distance and stamina. We would like to thank our sponsors, without whom this would not have been possible: the Kennel Club, Skinner's Dog Food, Dick White Referrals and Burrow's Motor Company, Toyota."
Caroline Kisko, Kennel Club Secretary said: "We are very proud of Field Trials Team GB and their performance in Serbia, which will stand them in good stead for future World Championship competitions."
For further press information or interview requests please contact
The Kennel Club Press Office
If you are a journalist and would like more information please click here.
Blog - The Kennel Club Charitable Trust
Facebook - www.facebook.com/Kclovesdogs
Twitter - twitter.com/kclovesdogs
Copyright © The Kennel Club Limited 2017. The unauthorised reproduction of text and images is strictly prohibited.


text:
Posts Tagged 'gogodex.com'
Advertisement :
Sponsered Links :
Now List Your Automobile Industry Website On Gogodex Directory!
Submitted by nancymarshal • September 11, 2012
www.gogodex.com - Now l ist your a uto mobile industry website on gogodex.com directory. You may also find all the sub related top ics on auto industry from gogodex . It will generate numerous of links, traffics and listings for your websites. ...
Advertisement :


text:
Date for "Meet the Snappers" Event Set
March 7, 2017 4:49 PM ET
BELOIT, WI - The annual "Meet the Snappers" event will take place April 4, 2017, the Beloit Snappers announced Monday. This year's meet and greet will take place once again at Beloit Memorial High School (1225 Fourth Street, Beloit). Doors will open up to the public at 5:30 p.m. and the event will run until 7 p.m.
Headlining this season's event will be new Snappers manager Scott Steinmann. Steinmann spent 20 years in the Seattle Mariners organization as a player and coach. He brings nine seasons of managerial experience to Beloit, most recently with the Clinton LumberKings of the Midwest League in 2015.
"I'm excited to introduce Scott as our new manager," says Snappers General Manager Seth Flolid. "His experience as a coach and understanding of the community aspect of Minor League Baseball will both benefit the Snappers this season."
Though the team is unsure exactly who will be suiting up for Beloit once Opening Day rolls around, this will be the community's first opportunity to be up close and personal with the 2017 team. Players will also be available for autographs. The Snappers coaching and front office staffs will join the players at the event.
"This is always such a great event," states Flolid. "For a lot of our fans, the interest in the players themselves is as important as their performance on the field."
Tickets to "Meet the Snappers" will be $5 per person and kids ages 4 and under can get in free. Tickets can be purchased in advance through the Snappers via phone at (608) 362-2272 or in person at Pohlman Field (2301 Skyline Drive, Beloit). New team merchandise will be available to purchase at the 2017 "Meet the Snappers" event. The menu for the evening will be traditional ballpark fare.
The Beloit Snappers are a member of the Midwest League and have been the Single-A affiliate of the Oakland Athletics since 2013. Opening Day for the Snappers 36th season is April 6, 2017 at Pohlman Field as the Snappers host the Cedar Rapids Kernels. Tickets for Opening Day are quite the steal! Just $2.50 thanks to the temperature on the morning Individual Tickets went on sale February 27. For more ticket information, contact the Snappers office at (608) 362-2272 or on our website, www.snappersbaseball.com.
View More


text:
img/ 458079
Download the Document
File Size: 5.41 MB
File Size: 5.41 MB
We hope you like our service. Recommend it to your friends.
Table of contents
View All
• Important Information About Your TV
• Important Safeguards
• Television Overview
• Package Contents
• Special Features of Your TV
• TV Front Panel
• TV Back Panel
• TV Set-Up
• Guidelines for Setting Up and Using Your New Widescreen TV
• Installing the Remote Control Batteries
• When You First Power On the TV
• Initial TV Setup
• Setting Up TV Inputs
• Controlling A/V Receiver Sound Volume
• Using the TV with a Personal Computer
• TV Connections
• Before you Be
• HDTV Cable Box or Satellite Receiver with Component Video
• Standard Cable Box, Satellite Receiver, or Other Device...
• HDMI Device (Cable Box, Satellite Receiver, DVD Player, or...
• Wall Outlet Cable (no cable box)
• Antenna with a Single Lead
• DVD Player with Component Video
• DVI Video Device (Cable Box, Satellite Receiver, DVD...
• VCR to an Antenna or Wall Outlet Cable
• VCR to a Cable Box (Audio & Video)
• A/V Receiver (Sound System)
• Older Cable Box
• Camcorder
• TV Operation and Features
• Choosing a Viewing Source
• Sleep Tim
• Remote Control
• ChannelView™ Channel Listings
• Status Display
• FAV (Favorite Channels)
• TV Signals and Display Formats
• JPEG Photos and the USB Photo Port
• Photos and Moving Video as Composite Video
• TV Menu Settings
• Remote Control Keys for the TV Menu System
• AV Menu
• Video Menu
• Audio Menu
• Captions Menu
• Setup Menu
• Inputs Menu
• Lock Menu
• Setting or Resetting a Pass Code
• Parent Menu
• Other Menu (Alternate Rating System)
• Bypassing TV Locks
• NetCommand
• About NetComma
• IR Emitter Placement (NetCommand®)
• Initial NetCommand Setup for Most Devices
• Add or Remove Device Keys from NetCommand Control
• NetCommand Specialized Device Keys
• Operating NetCommand-Controlled Devices
• Setting Up NetCommand Control of an A/V Receiver
• Appendices
• Appendix A: Specifications
• Appendix B: Bypassing the Parental Lock
• Appendix C: Lamp-Cartridge Replacement and Cleaning
• Appendix D: Programming the Remote Control
• Appendix E: Troubleshooting
• Trademark and License Information
• Mitsubishi TV Software
• Mitsubishi DLP™ Projection Television Limited Warranty
View All
Ads related to Mitsubishi WD-65733
Mitsubishi wd-65733 (65") DLP TV? - Yahoo Answers
My 65 inch DLP Mitsubishi TV has white spots all over the screen. I know that I need to replace the DMD (digital micromirror device). My question is, do I ...
Mitsubishi WD-C657 DLP has white spots on screen - Page 9 ...
I have owned a WD 65733 for about four years. A white dot came on the screen about a month ago and a new one appears every couple of days. I called Mitsubishi and ...
Mitsubishi WD-65733 Light Engine Replacement - AVS Forum
When white and black dots appeared on my Mitsubishi WD-57733, I researched it and found that it was a failing light engine that caused the dots...
Ads related to Mitsubishi WD-65733


text:
Executive Platform
- Executive Platform
Cisco Joins Eclipse Foundation
We are pleased to announce that we are joining the Eclipse Foundation, the leading open source organization whose projects areRead More
- Executive Platform
GREEN on St. Patty's Week
First, Happy St. Patrick's Day. I, of course, forgot to don a green shirt…or socks…or anything, so even though IRead More
- Executive Platform
Al Gore and John Chambers on Climate Change and Technology Innovation
Nobel Laureate, Oscar Winner and former Vice President Al Gore will join Cisco Chairman and CEO John Chambers in aRead More
- Executive Platform
What is Your Digital Footprint?
The New York Times BITS blog today wrote about a new study out by IDC that says that at, "281Read More
- Executive Platform
Apple iPhone Enterprise-ready with Cisco VPN
Today at Apple's Headquarters in Cupertino, CA, Apple's CEO Steve Jobs and SVP of Marketing Phil Schiller announced new iPhoneRead More
- Executive Platform
Web 2.0 Marketing Campaign for the ASR 1000 Series
Suraj Shetty, senior director of service provider marketing at Cisco discusses the importance of web 2.0 marketing as both aRead More


text:
To try the thousands of add-ons available here, download Mozilla Firefox, a fast, free way to surf the Web!Close
Welcome to Firefox Add-ons.
Choose from thousands of extra features and styles to make Firefox your own.Close
Meet the QrCodeR Developer
Why was QrCodeR created?
After a few weeks of getting my first got an Android phone, I got frustrated of using web services to encode QrCodes of what I needed to send to my phone. 'There must be an easier way', I thought. I then looked for an Firefox Addon that got the job done, but their UI was just too complex for something so simple (Yes, I like to keep my Firefox lean and fast :D). I then started working on QrCodeR, keeping it as simple as possible.
What's next for QrCodeR
Future plans for QrCodeR include finding a better way to save the encoded qrcode and adding any other feature the users suggest or request ;)
About the Developer
|Software Engineer
|User since
|July 10, 2008
|Number of add-ons developed
|1 add-on
|Average rating of developer's add-ons
|Rated 5 out of 5 stars
To create your own collections, you must have a Mozilla Add-ons account.


text:
Following a recent realignment of the Divisions within Mandate, the Dublin South West Division has had a number of changes both in personnel and in the geographical area it covers.
The official dealing with all areas within the Division is Dave Moran, Divisional Organiser supported by Terri Gaffney and Barbara Anderson Admin Assistants.
The Dublin South West Division represents all employments in the retail sector including the licensed trade. It now covers the geographical area encompassing: Dublin City Centre South, Upper Baggot Street, Rathmines, Ranelagh, Rathgar, Crumlin, Walkinstown, Kilnamanagh, Ballinteer and Knocklyon.
We are available to members and potential members and offer a full range of Industrial Relations services and can be contacted by the e-mail addresses above or by phone at 01-8746321.
All News
Monday 11 September 2017, 09am
The Union Representative QQI Level 5 Training Course is for shop stewards/union representatives who
Union Representative Introductory
Monday 18 September 2017, 09am
The Union Representative Introductory Training Course is
View all events
Monday 18 September 2017, 09am
The Union Representative Introductory Training Course is
View all events
View all events


text:
So guys, I'm finishing my challenge run, where I don't level up and I was thinking about making a save-file and publish it here at the wiki, so anyone could start at NG+.
Of course all the souls, items, weapons and armour wouldn't be included in the savefile, only the starting armor non-upgraded.
Sadly, in this playthrough I bought some sorceries, miracles and pyromancies out of boredom, so they would be available to the player at the start of the game.
What you guys think about it? This blog post is more like poll, so comment what you think.


text:
6840 Cornell Street, Portage MI, 49024
Sold Price:
2 beds , 2 Full baths
1,831 sqft
Status: Closed
Last Updated: 7/23/2017 7:41 AM
Description for 6840 Cornell Street Portage, MI 49024
You will not BELIEVE the value of this delightful home w BONUS basement space! Brand new fridge, new cabinetry w family-friendly features, new kitchen floors, newer water heater, new vanity, newer ceiling fans, newer carpet in basement, newer windows in basement, newer sewage pump - maintained to a T. Hardwood floors throughout under carpet, perfect for anyone. HUGE main floor laundry room, mud access, award-winning Portage Schools, centrally located w direct access to Celery Flats! Extra space in basement, second 2-car garage w electricity PLUS 2-story outbuilding! Several parking spaces on top of the three cars of garage space! Enjoy the large fenced in backyard or relax in the inviting front porch among friendly neighbors. This is a must-see home and a great investment! See it TODAY!
Sold Price:
Sold Date:09/11/2015
Portage City
2 Full
1,831 (approx)
Listing Information
Portage City
Public Water Service
Public Sewer
Cable TV, Electric, Natural Gas, Telephone
School Information
Room Information
Eat-In Kitchen, Butler Pantry
Interior Features
Dishwasher, Microwave, Range, Refrigerator
Ceramic, Wood
Central Air, Ceiling Fan(s)
Gas Heat, Forced Air
Basement, Full
Wood Floors
Exterior / Lot Features
Extra Storage, Paved Road, Public Roads
Driving Directions
Romence Road from Westnedge (West, toward Oakland) to Cornell (North to home)
Financial Considerations
Listing Price History
Portage Real Estate
Portage is located in Michigan. Portage, Michigan 49024 has a population of 48,177.
The median household income in Portage, Michigan 49024 is $55,050. The median household income for the surrounding county is $46,356 compared to the national median of $53,482. The median age of people living in Portage 49024 is 37.3 years.
Loading nearby sales and history ...
Ask a Question?
Start a no spam email conversation
Nearby homes for sale
Portage Real Estate
Nearby Communities


text:
I wish I were joking. It's been this way for years; Casey wrote about this in 2008.
This mask works for events like WM_LBUTTONDOWN, but it does not work for the mouse motion events e.g. WM_INPUT. If you want to take input both from touch and the mouse, you need to disambiguate the real WM_INPUTs from the fake ones. Through a process of experimentation with message flags, I landed on this:
#define MOUSEEVENTF_FROMTOUCH 0xFF515700
if ((GetMessageExtraInfo() & MOUSEEVENTF_FROMTOUCH)
// Skip message
if ((GetMessageExtraInfo() & 0x82) == 0x82) { /* ignore event */ }
It seems to work for now, but who knows if that will mysteriously break in some future version of windows.
Nicely, if your application handles WM_POINTER messages, you will not get any of this mouse emulation stuff or WM_TOUCH, so all this ugliness disappears. If it is okay to make Windows 8 your minimum specification, I recommend using WM_POINTER and staying far away from WM_TOUCH.


text:
Friction is the force resisting the relative lateral (tangential) motion of solid surfaces, fluid layers, or material elements in contact. It is usually subdivided into several varieties:
- Dry friction resists relative lateral motion of two solid surfaces in contact. Dry friction is also subdivided into static friction between non-moving surfaces, and kinetic friction (sometimes called sliding friction or dynamic friction) between moving surfaces.
- Lubricated friction or fluid friction resists relative lateral motion of two solid surfaces separated by a layer of gas or liquid.
- Fluid friction is also used to describe the friction between layers within a fluid that are moving relative to each other.
- Skin friction is a component of drag, the force resisting the motion of a solid body through a fluid.
- Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation.
Friction is not a fundamental force, as it is derived from electromagnetic force between charged particles, including electrons, protons, atoms, and molecules, and so cannot be calculated from first principles, but instead must be found empirically. When contacting surfaces move relative to each other, the friction between the two surfaces converts kinetic energy into thermal energy, or heat. Contrary to earlier explanations, kinetic friction is now understood not to be caused by surface roughness but by chemical bonding between the surfaces. Surface roughness and contact area, however, do affect kinetic friction for micro- and nano-scale objects where surface area forces dominate inertial forces.
|Includes CC-BY-SA content from Wikipedia's Friction article (authors)


text:
|Home > Hatsie
♀ Hatsie
What does Hatsie mean?
Hatsie [hat-sie] as a girls' name is of Old German derivation, and the meaning of the name Hatsie is "home leader". Hatsie is a version of Harriet (Old German): feminine of Harry, from Henry. Hatsie is also a variant of Henrietta (Latin, French, Old German).
VARIANTS Hatsy, Hatsey, Hatsee
RELATED FORMS VIA HARRIET, HENRIETTA Ettie▼, Halle▼, Hallie, Harrie, Hat, Hattie▼, Hatty, Henie, Hennie, Henrie, Hette, Hettie▼, YettieCREATIVE FORMS
(female) Hansie, Hasie, ..
(male) Hatson, Hatwin, .. MIDDLE NAME PAIRINGS
Hatsie Raina (H.R.), ..
How popular is Hatsie?
Hatsie is an uncommonly occurring given name for females. Hatsie is also an uncommon last name for all people. (2000 U.S. CENSUS)
Which version is better?with its source forms and related girl names. Hattie (#488 A YEAR AGO), Hallie (#566), Halle (#916), Harriet (#1314), Hettie, Henrietta, Hennie and Ettie are the popular varying forms of Hatsie (NOT RANKED) rated in the Top 2000. Other variants, like Hatsee, are seldom used. Adoption of these relations of Hatsie was common among parents during 1880-1889 (USAGE OF 0.9%) and has become much diminished since (USAGE 0.1%, 91.1% LESS), with forms such as Hettie becoming somewhat outmoded. (2015 U.S. SSA RECORDS)
Similar NamesRecommended names are Betsie, Caisie, Casie, Cassie▼, Cathie, Catie, Caysie, Daisie, Darsie, Dasie, Hadwig, Haelie, Hailie▼, Halie▼, Hannie, Hansine, Harlie, Haylie▼, Hepsie, Hittie, Kasie, Kassie, Kathie▼, Katie▼, Kaysie, Lassie, Maisie▲, Mattie▼, Nattie, Pansie, Pattie▼, Taisie, Tassie and Tatie. These names tend to be more frequently used than Hatsie.See names in meaning and etymology.


text:
Nearly every radiology department or practice will be affected by accountable-care organizations (ACOs)—because even if it chooses not to become part of one or more ACOs, it will probably be competing with them. Since some types of ACOs will be granted the ability to sidestep current price-fixing and self-referral restrictions, according to proposed ACO antitrust regulations¹ released on April 19, 2011, the competition between ACO participants and nonaligned groups could become intense. ACOs are permitted to serve commercially insured patients as well as Medicare/Medicaid enrollees (under the same loosened self-referral restrictions), so they are likely to be competing, sooner or later, for most of the imaging volume in any area.
In "Building Regulatory and Operational Flexibility Into Accountable Care Organizations and 'Shared Savings,'"² published in Health Affairs, Steven M. Lieberman and John M. Bertko predicted much of what the March 31 proposed rule³ for ACOs and the April 19 antitrust proposal¹ would contain. Lieberman is president of Lieberman Consulting Inc (Bethesda, Maryland) and Bertko is a senior fellow at the LMI Center for Health Reform (McLean, Virginia).
Both authors are visiting scholars at the Brookings Institution's Engelberg Center for Health Care Reform (Washington, DC). They are working on a collaboration between the center and the Dartmouth Institute for Health Policy & Clinical Practice (Lebanon, New Hampshire) to develop workable models for ACOs.
They write, "ACOs have the potential to lower costs, improve the quality of care, facilitate delivery-system reform, and promote innovation in health care." Those hopes first led to the creation of ACOs in 2010's Patient Protection and Affordable Care Act (PPACA).
In January 2012, ACOs can begin three years of participation in Medicare's Shared Savings Program, which is expected to return bonuses of $800 million during that period to ACOs that save CMS money. ACOs that cost Medicare more than it expects to pay could be required to return $40 million to CMS, however.
In return for fee-for-service payment, ACOs must provide comprehensive care to at least 5,000 Medicare enrollees, either by incorporating all necessary services in their organizations or by paying for non-ACO services. Enrollees must be free to choose providers, but ACOs will pay those providers, even if they are outside the ACO. CMS will assign Medicare enrollees to the ACOs to which their primary-care providers belong, and ACOs will have no ability to reject any Medicare beneficiary (but enrollees can reject an ACO by changing primary-care providers).
ACOs that meet predetermined quality standards will be eligible for bonuses of up to 60% of Medicare savings if they are willing to risk repaying CMS 10% of its predicted cost of care, if they fail to save Medicare any money. If they are unwilling to take that risk for the program's first two years, they can still qualify for bonuses of up to 50% (but during the program's third year, they will have to return up to 7.5% of excess costs of care to CMS).
ACOs must also meet CMS criteria for organizational, legal, and management structure, and they are required to provide cost and quality data (and have the necessary information systems in place). Comments on the antitrust proposal and the ACO proposal will be accepted until May 31 and June 6, respectively.
Radiology's Prospects
Because ACOs will be paying for the services of specialists (including radiologists), many ACOs will encourage radiology departments and groups to become affiliated with them—but ACOs are not allowed to create exclusive arrangements with specialists, so radiology groups can expect to work with multiple ACOs, instead of being tied to one (as some had previously planned).
The effect of ACOs on imaging volume is difficult to predict. Many ACOs will probably attempt to limit costs by reducing utilization of expensive services such as advanced imaging, but others might increase imaging volume, particularly for screening exams, in an attempt to improve documented quality of care (and reduce future costs of care through earlier diagnosis). Imaging providers might be wise to ensure that ACOs forming in their areas are fully aware of what they can offer, especially since the proposed relaxation of self-referral prohibitions1 would make in-office imaging outside radiology more attractive to some ACOs.
Providers participating in ACOs are not allowed to restrict,


text:
|Message view
|« Date » · « Thread »
|« Date » · « Thread »
|"Geir Magnusson Jr." <g...@pobox.com>
|Re: [drlvm][win32] Kernel tests crashes on win32
|Wed, 22 Nov 2006 03:04:58 GMT
Gregory Shimansky wrote: > On Wednesday 22 November 2006 03:01 Geir Magnusson Jr. wrote: >> I've added that test to the exclusion lists for windows. > > Yes I noticed. I am actually surprised that it has helped. It appears that > just one test causes the crash. In my investigation I was quite sure that the > problem appears because of GC or finalization, so the crash should be > happening in the subsequent tests on GC. Maybe this test just triggers the > problem... I'm still working on trying to figure out. I managed to get it to hang under windows in the interpreter. I'll try and figure that out later. As to triggering... I dunno - this is hard. The damage could easily have been caused long before the problematic test case, and the test that crashes things is just simply showing the damage. Thanks for sticking with this. > >> We can now run complete so can start monitoring for regressions (as well >> as fix the breakage for the tests that are excluded...) > > The reason why I didn't want to exclude gc.LOS was that is works just fine on > windows 2003 server, hangs only on XP (threading in kernels seems to be quite > different in them, there is also a known difference between windows 2003 > server and windows 2003 server SP1). But excluding on such platform selection > was not possible and still isn't. So I hoped that the test would be rather > fixed than excluded. However I agree that a test which fails for several > months already shouldn't stand in the way and excluding it even for all types > of windows is the right thing. If we can somehow distinguish between 2003 and XP, we can exclude using these exclude lists now. > > Let's not allow any regressions again. But introducing test failures even > without changing the tests themself should not be done unannounced and > undiscussed. I was about to revert a JIRA patch when I saw tests crash on > windows with new mode. Huh? geir
|View raw message


text:
You have no items in your shopping cart.
E Cig Flavors. Electronic Cigarette Liquids
At HotVapes, we make our own liquids from special recipes that we have developed. They are hand-mixed with ingredients that we choose with lots of love and care so that you can enjoy them like we do. You can feel good about our USA made e cig liquid.
You may want to cut down on smoking cigarettes, or maybe you want to quit. We know from our own experience that our HotVapes personal vaporizers, often called e-cigs can help you do just that.
When you see our 120 flavors plus, you'll find many e cig flavors that you'll want to try. Our HotVapes (HV) Big Heart Flavors are our main line of yummy liquids. Some days you may want a tobacco flavor with or without nicotine, and another day you'll go for our Blueberry Fest. You'll want that flavor all day, or go for Caramel Apple or Cherry Sucka.
We also have tasty organic flavors like Organic Bananas Foster or Organic Almond Cream. We also make HV Shisha Flavors, including Apple Shisha, Pistachio Shisha, and more.
Each bottle is either 17ml or 34ml with your choice of no-nicotine, 3mg, 6mg, 12mg, 18mg, or 24mg. Try out Blueberry Fest, Our Why 5, Cinnamon Arbalest, Café Filbert, and Carnival. All are totally unique flavors. They're some of our favorites, and we know that you'll love them too.
If you enjoy desserts, you'll enjoy our delicious flavors Whisk Licker, Banana Fandango, Hellen's Chocolate Slurry, Coconut Dream Pie, and "Some More." You choose the nicotine strength or none at all.
Order any flavors from our three lines of liquids that include HV Big Heart Flavors, HV Organic Flavors, or HV Shisha Flavors. You may just find your favorite new flavor! They are sent to you in dropper bottles of 17ml or 34ml.