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Heejun Han Doesn't Hit the Mark With 'Right Here Waiting' on 'American Idol'
This week on 'American Idol' we met contestant Heejun Han's adorable parents and watched his Mom tear up as she recalled that how her baby Heejun always woke up with a smile on his face.
Han took the stage smiling tonight as he prepared to take on a song from the year he was born, choosing 'Right Here Waiting' by Richard Marx. While worried in his practice with will.i.am about his accent hindering the performance, it didn't stop the jokester from asking the mentor if he could get fellow Black Eyed Pea's member Fergie's phone number.
Well he may be prepared to do whatever it takes (even if his heart breaks) America might not be waiting to vote Han as their idol. The judges had mixed reactions, Jennifer Lopez and Steven Tyler giving positive but lackluster feedback and Randy Jackson telling Han "I didn't really enjoy this at all. It was pitchy all over the place and it felt like you were out of breath the whole time." He went on to say that he missed Han's urban R&B swag, and felt the singer chose the wrong song and went "too pop." Tyler agreed that it wasn't a great song choice, but said he loved it anyways.
Lopez had better words for Han calling his tone "special and gorgeous" and said while she could feel him struggling throughout the performance she still adored it. While he gave it his all and put his heart in the song, we're not sure if that's going to be enough to keep him in the game. He's got the chops when it comes to singing and certainly knows how to entertain, but we're waiting for the cane to come and pull him off the stage.
Watch Heejun Han Perform 'Right Here Waiting' on 'American Idol'


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Episode 08 (1936 p3) of Danceable Tangos of the Year airs on Mon (02/22) at 19h CET (1pm EST), repeats on Wed (02/24) at 23h CET (5pm EST).
"Danceable Tangos of the Year" is a special programming of Argentine Tango Radio, Budapest: www.argentinetangoradio.com . This 52 episode, weekly series aims to showcase examples of danceable Argentine tangos, valses and milongas, progressing from 1927 up until last year.
New episodes of "Danceable Tangos of the Year" come out every Monday at 7pm, Central European Time (or 1pm Eastern Standard Time); these episodes then get repeated every Wednesday at 11pm, Central European Time (or 5pm Eastern Standard Time).

subset: commoncrawl


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Attorneys for Appellants Amici Curiae
Michael L. Carmin Indiana Civil Liberties Union
Andrews Harrell Mann Carmin & Parker J. Alexander Tanford
Julia Blackwell Gelinas Bloomington, Indiana
Nelson D. Alexander Kenneth J. Falk
Locke Reynolds LLP Indianapolis, Indiana
Indianapolis, Indiana
Indiana Association of Cities and Towns
Attorneys for Appellee Michael J. Lewinski
Linda Runkle, Corporation Counsel Timothy E. Ochs
Patricia S. Bernens, City Attorney Tanya D. Marsh
R. Michael Flory, Asst. City Attorney Ice Miller
Bloomington, Indiana Indianapolis, Indiana
City of West Lafayette, Indiana
Robert L. Bauman
West Lafayette City Attorney
Pamela J. Hermes
West Lafayette Assistant City Attorney
Gambs, Mucker & Bauman
Lafayette, Indiana
No. 53S01-0209-CV-472
Appeal from the Monroe Circuit Court, No. 53C04-9604-OV-350
The Honorable Elizabeth N. Mann, Judge
On Petition To Transfer from the Indiana Court of Appeals
September 23, 2003
This appeal challenges the trial court's determination that a local zoning ordinance restricting
the number of unrelated adult persons per dwelling in a single-family residential zone
does not violate the Privileges and Immunities Clause of the Indiana Constitution and
was not an ultra vires act. We affirm.
Peter Dvorak is the owner of a residential property located at 107 S. Bryan Avenue in Bloomington. On April 23, 1996, the City filed a complaint against Dvorak and the other defendants-appellants, tenants of Dvorak (hereinafter collectively "Dvorak"), claiming that they violated a zoning ordinance in the Bloomington Municipal Code which prohibits the property from being occupied by more than four adults unrelated by blood, marriage, or adoption. See footnote The Citys complaint sought to enjoin future use of the property inconsistent with the ordinance and to impose a fine of $2,500 per day from the time the violation began until the time it ceased. Dvorak filed a motion for summary judgment, claiming that the ordinance was void as an ultra vires act and that it violated Article 1, Section 23, the Equal Privileges and Immunities Clause, of the Indiana Constitution. After a hearing and the submission of briefs by the parties, the trial court denied the motion, finding that the ordinance was neither ultra vires nor unconstitutional. At Dvorak's request, the trial court certified the ruling for interlocutory appeal. The Court of Appeals accepted the appeal, vacated the decision of the trial court, and remanded for further proceedings, noting that the trial court had relieved the City of its duty to answer an interrogatory seeking "the City's justification(s) and rationale(s)" for the ordinance, and holding that Dvorak "should be given a reasonable opportunity for discovery in order to determine what goals the Ordinance was designed to promote." Dvorak v. City of Bloomington, 702 N.E.2d 1121, 1126 (Ind. Ct. App. 1998). Thereafter, in a bifurcated bench trial on the issues of constitutionality and whether its adoption was an ultra vires act, the trial court entered judgment upholding the ordinance. Upon review of this judgment, the Court of Appeals reversed, finding the zoning ordinance unconstitutional under Section 23. Dvorak v. City of Bloomington, 768 N.E.2d 490 (Ind. Ct. App. 2002). We granted the City's petition for transfer. Dvorak v. City of Bloomington, 783 N.E.2d 695 (Ind. 2002) (table).
Dvorak contends on appeal that the zoning ordinance violates Section 23 and that
its adoption was an ultra vires act.
The requirements of Article 1, § 23 govern not only state statutes, but
also the enactments and actions of county, municipal, and other governmental agencies and
their equivalents. See, e.g., IHSAA, Inc. v. Carlberg, 694 N.E.2d 222, 231
(Ind. 1997); Haas v. South Bend Comm. Sch. Corp., 259 Ind. 515, 289
N.E.2d 495 (1972); Phillips v. Officials of Valparaiso, 233 Ind. 414, 120 N.E.2d
398 (1954); Kersey v. City of Terre Haute, 161 Ind. 471, 68 N.E.
1027 (1903); Graffty v. City of Rushville, 107 Ind. 502, 509, 8 N.E.
609, 612 (1886); Indianapolis v. Clint's Wrecker Serv., Inc., 440 N.E.2d 737, 744
(Ind. Ct. App. 1982). But see Bd. of Comm'rs of the County
of Howard v. Kokomo City Plan Comm'n, 263 Ind. 282, 294, 330 N.E.2d
92, 100 (1975).
The Privileges and Immunities Clause of the Indiana Constitution states, "[t]he General Assembly
shall not grant to any citizen, or class of citizens, privileges or immunities,
which, upon the same terms, shall not equally belong to all citizens."
Ind. Const. art. I, § 23. In Collins v. Day, we analyzed
the common understanding of the framers and ratifiers of Section 23 and early
cases implementing that section, concluding as follows:
To summarize, we hold that Article I, Section 23 of the Indiana Constitution imposes two requirements upon statutes that grant unequal privileges or immunities to differing classes of persons. First, the disparate treatment accorded by the legislation must be reasonably related to inherent characteristics which distinguish the unequally treated classes. Second, the preferential treatment must be uniformly applicable and equally available to all persons similarly situated. Finally, in determining whether a statute complies with or violates Section 23, courts must exercise substantial deference to legislative discretion.
644 N.E.2d 72, 80 (Ind. 1994).
Directing their first two claims to the first requirement in Collins, Dvorak contends:
No inherent distinctions exist between equal numbers of related and unrelated adults that are reasonably connected to the accomplishment of the Ordinance's objectives of reducing trash, noise, and traffic and maintaining core neighborhoods by reducing adult population density.
. . . .
No inherent distinctions exist between equal numbers of related and unrelated adults that are reasonably connected to family values or providing healthful surroundings for family life.
Br. of Appellants at 12, 18. Dvorak's third claim involves the second
Collins requirement: "[t]he Ordinance permits some non-family groups to live in single-family
zones but denies this privilege to other similarly situated groups." Id. at
As a preliminary matter, we note that Dvorak's constitutional arguments place considerable emphasis
upon the alleged failures of the City to establish or demonstrate that disparate
treatment of different classifications under the ordinance was reasonably connected to the City's
legislative goals. Because it is Dvorak, not the City, who asserts this
constitutional challenge, however, there is no burden upon the City to demonstrate that
the ordinance is constitutional. Rather, the burden is entirely upon Dvorak to
overcome the presumption of constitutionality and to establish a constitutional violation. Sims
v. United States Fid. & Guar. Co., 782 N.E.2d 345, 349 (Ind. 2003);
Boehm v. Town of St. John, 675 N.E.2d at 321; Collins, 644 N.E.2d
at 81.
Dvorak asserts that the ordinance, Bloomington Municipal Code § 20.02.01.00, excludes from single-family residential districts households consisting of more than three adults not related by blood, marriage or legal adoption. Br. of Appellants at 4. The Bryan Avenue property was "grandfathered" to permit four unrelated adults to occupy the property. Appellants' App. at 143. Dvorak does not challenge the propriety of the City's creation of single-family residential districts, but claims a constitutional violation contending that the ordinance unequally treats two different classes: households comprised of four or more related adults and those comprised of four or more unrelated adults. Dvorak argues that the City's purposes in enacting the ordinance are not reasonably related to any inherent characteristics that distinguish these two classes.
This argument places a strained construction on Collins, which requires only that the "the disparate treatment accorded by the legislation," not the purposes of the legislation, "be reasonably related to the inherent characteristics which distinguish the unequally treated classes." Collins, 644 N.E.2d at 79; Boggs v. Tri-State Radiology, Inc., 730 N.E.2d 692, 696 (Ind. 2000) (considering whether special medical malpractice statute of limitations was reasonably related to the inherent characteristics distinguishing medical malpractice victims from other tort victims); McIntosh v. Melroe Co., 729 N.E.2d 973, 981 (Ind. 2000) (deciding whether the products liability statute of repose is reasonably related to the inherent characteristics that define the distinction); IHSAA, Inc., 694 N.E.2d at 240 (determining whether limited athletic eligibility is reasonably related to inherent distinctions distinguishing transfer students from other students). While it is the treatment, not the legislative purpose, which must be reasonably related to the inherent distinctions between the classes, the legislative purposes may be a factor considered in making this determination. See, e.g., Sims, 782 N.E.2d at 353-54.
We therefore find this appeal to present the following appellate issue: whether Dvorak
has demonstrated either (1) that the ordinance's disparate treatment of two classes of
persons is not reasonably related to their distinguishing inherent characteristics, or (2) that
the preferential treatment accorded one of the classes is not uniformly applicable and
equally available to all persons similarly situated.
As to the first issue, the disparate treatment provided by the ordinance is
one of exclusion. Unlike households comprised of four or more adults related
by blood, marriage or legal adoption, similar households comprised of four or more
adults not so related are prohibited in single-family residential zones. Thus, the
issue is whether this exclusion is reasonably related to the characteristic distinguishing these
two classeswhether the members of a household are related by blood, marriage, or
legal adoption. The answer is self-evident: limiting multiple-adult households in single
family residential zones to families, and excluding non-families, is reasonably related to the
difference between families and non-families. To put it another way, considering whether
groups are or are not families is obviously related to determining whether to
exclude them from districts zoned for family residential use.
In addition to claiming that the Bloomington ordinance violates the first prong of
Collins, Dvorak also contends that it is invalid under the second Collins prong:
whether the preferential treatment accorded one of the classes is uniformly applicable
and equally available to all persons similarly situated. Dvorak argues that the
ordinance permits some non-family groups, specifically four college students living together in a
house previously occupied by four other students before the ordinance was enacted, to
live in a single-family zone but denies this privilege to other similar groups
unable to locate such a "grandfathered" house, contrary to the second prong of
the Collins test.
This isolated occurrence is insubstantial and does not render the ordinance contrary to
Section 23. As we observed in Collins:
Exact exclusion and inclusion is impractical in legislation. It is almost impossible to provide for every exceptional and imaginary case, and a legislature ought not to be required to do so at the risk of having its legislation declared void, even though appropriate and proper as applied to the general subject upon which the law intended to operate.
644 N.E.2d at 80, (quoting Cincinnati, Hamilton & Dayton Ry. Co. v. McCullom, 183 Ind. 556, 561, 109 N.E. 206, 208 (1915) (citations omitted)).
Under the Bloomington ordinance, any persons who are related by blood, marriage, or
adoption may reside in a single dwelling in the zoning classification, as may
up to three unrelated adults. The ordinance is uniformly applicable and equally
available to all persons similarly situated.
We conclude that the Dvorak defendants have not carried their substantial burden to
demonstrate that the challenged ordinance violates the Privileges and Immunities Clause of the
Indiana Constitution.
The zoning enabling legislation declares that "a unit wanting to exercise planning and
zoning powers in Indiana must do so in the manner provided by this
chapter." Ind. Code § 36-7-4-201(a). The relevant objectives of the statute
are stated in sub-section (b):
The purpose of this chapter is to encourage units to improve the health, safety, convenience, and welfare of their citizens and to plan for the future development of their communities to the end:. . . .(2) That new communities grow only with adequate public way, utility, health, educational and recreational facilities;. . . .(4) That residential areas provide healthful surroundings for family life . . .
I. C. § 36-7-4-201(b). In addition, other enabling legislation requires that zoning ordinances must be adopted for specific purposes, including "promoting the public health, safety, comfort, morals, convenience and general welfare." I.C. § 36-7-4-601(c)(3). To this end, the zoning ordinances may "regulate how real property is developed, maintained and used," including the implementation of "standards for population density and traffic circulation" and "any other provisions that are necessary to implement the purposes of the zoning ordinance." I.C. § 36-7-4-601(d)(2)(I)-(J).
With the adoption of the Indiana Home Rule Act, the legislature "abrogated the
traditional rule that local governments possessed only those powers expressly authorized by statute."
City of Gary v. Indiana Bell Tel. Co., Inc., 732 N.E.2d 149,
153 (Ind. 2000). The Home Rule Act expressly broadens a governmental unit's
authority to include not only "[a]ll powers granted it by statute," but also
"[a]ll other powers necessary or desirable in the conduct of its affairs even
though not granted by statute." I.C. § 36-1-3-4(b). The Act explicitly
declares that "[a]ny doubt as to the existence of a power of a
unit shall be resolved in favor its existence." I.C. § 36-1-3-3(b).
We have applied the Home Rule Act in construing the zoning authority of
governmental units. City of Crown Point v. Lake County, 510 N.E.2d 684,
685-86 (Ind. 1987).
Considering the enabling legislation and Home Rule Act, we reject Dvorak's claim that
the enabling legislation does not expressly authorize cities to make zoning distinctions between
different kinds of single housekeeping units based on familial status, or to regulate
the users of real estate rather than uses of real estate, and thus
the Bloomington ordinance is ultra vires. The legislature specifically authorized governmental units
to use zoning so that "residential areas provide healthful surroundings for family life,"
I. C. § 36-7-4-201(b)(4) (emphasis added), and in order "to promote the public
health, safety, comfort, morals, convenience and general welfare," I.C. § 36-7-4-601(c)(3).
The enactment of zoning ordinances that make distinctions based on familial relations of
the users of residential real estate is an integral component of implementing these
legislative objectives.
See footnote
Our conclusion is further reinforced by the Home Rule Act
which extends to each governmental unit "all other powers necessary or desirable in
the conduct of its affairs." I.C. § 36-1-3-4(b).


text:
" the snowy path to the old church ( night)© " by MassiSan ()
Vue Landscape posted on Feb 11, 2014
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" the snowy path to the old church ( night)© "
this scene started out as an render in daylight...but i had this idea coming up suddently and i gave it a try
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text:
Welcome to Alpha Complex! Welcome to the ranks of the Troubleshooters! Welcome to Paranoia!
As a Troubleshooter, you are a member of Alpha Complex's most expendable elite force. Tasked with finding trouble and shooting it, you will be hunting mutants, terrorists, traitors, [CLASSIFIED], secret societies, renegade bots, and DAIVs, which are [REDACTED]. You'll save Alpha Complex from its greatest threat, unless you accidentally become Alpha Complex's greatest threat.
Not enough Players Handbooks around your table? Troubleshooters causing trouble and shooting one another as they fight to gain access to the beloved Computer's wisdom? Fret no more, as a limited supply of Players Handbooks are nbow available for your lucky players!
Grab your own copy here: http://www.mongoosepublishing.com/rpgs/ ... dbook.html
Paranoia Players Handbook - Now Available Separately (for a while)
Paranoia is Fun. Other games are not Fun. Buy Paranoia.
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text:
As an academic researcher, Roger Howe knows what it's like to lose out to a worthy competitor in the never-ending scramble for federal funding. But as director of the National Nanotechnology Infrastructure Network (NNIN) at Stanford University in California, Howe is scratching his head over what he and others say is a recent nondecision by the National Science Foundation (NSF) to support what was to be the agency's next big step in providing support for the burgeoning field.
However, NSF says it's all a big misunderstanding and that it remains foursquare behind such collaborations.
NSF began funding NNIN in 2003 under a 10-year cooperative agreement, and this year NNIN is winding down its efforts to coordinate nanotech user facilities at 14 sites around the country. So in December 2012 NSF put out a solicitation describing its plans for a "next-generation" NNIN (NG-NNIN) that would broaden the collaboration to encompass researchers and educators in related fields.
The competition came down to Howe and a rival proposal from a team led by James Sturm of Princeton University. After pitching their visions last summer to a 12-member panel of outside experts assembled by NSF, each team went home and awaited word on who would claim the prize, expected to be $16 million a year for the next decade.
But last week both teams got an unexpected answer. Instead of picking a winner, NSF declared what Howe describes as a "no win outcome to the competition." The network announced the decision on its website last week, and Howe says he's not sure what will happen after NNIN exhausts its funding. "Needless to say, I feel that NSF's decision will have a significant negative impact on nano-related research and development." Adds Sturm: "We are both at a loss to explain what happened."
The answer is simple, according to NSF officials. "We have not made a formal decision, so asking that question is premature at this time," says Pramod Khargonekar, head of NSF's engineering directorate, which provides most of the funding for the network.
Khargonekar emphasizes that NSF has not altered its plans to support such a network. "NSF and the engineering directorate are committed to infrastructure support to enable transformative research in nanoscience and nanotechnology," he tells ScienceInsider. "We think it's important, and we will continue to provide support for it." As evidence, he cites the $15.5 million for NG-NNIN in NSF's 2015 budget request, as well as the identical amount in the NSF budget for the current fiscal year that ends on 30 September.
Khargonekar was less clear, however, about when that support will materialize. "We will make an announcement as we move forward," he says. "We have something we intend to do, but since our thinking is not mature, it would be premature to talk about it now."
Some of the community's concerns stem from the fact that NSF's contribution to the multiagency National Nanotechnology Initiative is shrinking. Its funding dropped from $466 million in 2012 to $410 million in the current year, and NSF's 2015 request maintains that level of support. Asked why, acting Director Cora Marrett said at a budget briefing yesterday that the "seeds" NSF has planted have grown to the point where nanotechnology is now a "mature" plant that has taken root.
"With some of these initiatives, you try to create networks to pull communities together. And if you have succeeded in doing that, you don't always need to continue with it as a special activity," she explained. "So yes, it's a high priority. But it's now pervasive enough to have been integrated into the core of what we do."
*Correction, 14 March, 4:36 p.m.: The link to NNIN's website has been corrected.


text:
Formal logic
Formal logic, the abstract study of propositions, statements, or assertively used sentences and of deductive arguments. The discipline abstracts from the content of these elements the structures or logical forms that they embody. The logician customarily uses a symbolic notation to express such structures clearly and unambiguously and to enable manipulations and tests of validity to be more easily applied. Although the following discussion freely employs the technical notation of modern symbolic logic, its symbols are introduced gradually and with accompanying explanations so that the serious and attentive general reader should be able to follow the development of ideas.
Formal logic is an a priori, and not an empirical, study. In this respect it contrasts with the natural sciences and with all other disciplines that depend on observation for their data. Its nearest analogy is to pure mathematics; indeed, many logicians and pure mathematicians would regard their respective subjects as indistinguishable, or as merely two stages of the same unified discipline. Formal logic, therefore, is not to be confused with the empirical study of the processes of reasoning, which belongs to psychology. It must also be distinguished from the art of correct reasoning, which is the practical skill of applying logical principles to particular cases; and, even more sharply, it must be distinguished from the art of persuasion, in which invalid arguments are sometimes more effective than valid ones.
General observations
Probably the most natural approach to formal logic is through the idea of the validity of an argument of the kind known as deductive. A deductive argument can be roughly characterized as one in which the claim is made that some proposition (the conclusion) follows with strict necessity from some other proposition or propositions (the premises)—i.e., that it would be inconsistent or self-contradictory to assert the premises but deny the conclusion.
If a deductive argument is to succeed in establishing the truth of its conclusion, two quite distinct conditions must be met: first, the conclusion must really follow from the premises—i.e., the deduction of the conclusion from the premises must be logically correct—and, second, the premises themselves must be true. An argument meeting both these conditions is called sound. Of these two conditions, the logician as such is concerned only with the first; the second, the determination of the truth or falsity of the premises, is the task of some special discipline or of common observation appropriate to the subject matter of the argument. When the conclusion of an argument is correctly deducible from its premises, the inference from the premises to the conclusion is said to be (deductively) valid, irrespective of whether the premises are true or false. Other ways of expressing the fact that an inference is deductively valid are to say that the truth of the premises gives (or would give) an absolute guarantee of the truth of the conclusion or that it would involve a logical inconsistency (as distinct from a mere mistake of fact) to suppose that the premises were true but the conclusion false.
The deductive inferences with which formal logic is concerned are, as the name suggests, those for which validity depends not on any features of their subject matter but on their form or structure. Thus, the two inferences (1) Every dog is a mammal. Some quadrupeds are dogs. ∴ Some quadrupeds are mammals. and (2) Every anarchist is a believer in free love. Some members of the government party are anarchists. ∴ Some members of the government party are believers in free love. differ in subject matter and hence require different procedures to check the truth or falsity of their premises. But their validity is ensured by what they have in common—namely, that the argument in each is of the form (3) Every X is a Y. Some Z's are X's. ∴ Some Z's are Y's.
Line (3) above may be called an inference form, and (1) and (2) are then instances of that inference form. The letters—X, Y, and Z—in (3) mark the places into which expressions of a certain type may be inserted. Symbols used for this purpose are known as variables; their use is analogous to that of the x in algebra, which marks the place into which a numeral can be inserted. An instance of an inference form is produced by replacing all the variables in it by appropriate expressions (i.e., ones that make sense in the context) and by doing so uniformly (i.e., by substituting the same expression wherever the same variable recurs). The feature of (3) that guarantees that every instance of it will be valid is its construction in such a manner that every uniform way of replacing its variables to make the premises true automatically makes the conclusion true also, or, in other words, that no instance of it can have true premises but a false conclusion. In virtue of this feature, the form (3) is termed a valid inference form. In contrast, (4) Every X is a Y. Some Z's are Y's. ∴ Some Z's are X's. is not a valid inference form, for, although instances of it can be produced in which premises and conclusion are all true, instances of it can also be produced in which the premises are true but the conclusion is false—e.g., (5) Every dog is a mammal. Some winged creatures are mammals. ∴ Some winged creatures are dogs.
Formal logic as a study is concerned with inference forms rather than with particular instances of them. One of its tasks is to discriminate between valid and invalid inference forms and to explore and systematize the relations that hold among valid ones.
Closely related to the idea of a valid inference form is that of a valid proposition form. A proposition form is an expression of which the instances (produced as before by appropriate and uniform replacements for variables) are not inferences from several propositions to a conclusion but rather propositions taken individually, and a valid proposition form is one for which all of the instances are true propositions. A simple example is (6) Nothing is both an X and a non-X. Formal logic is concerned with proposition forms as well as with inference forms. The study of proposition forms can, in fact, be made to include that of inference forms in the following way: let the premises of any given inference form (taken together) be abbreviated by alpha (α) and its conclusion by beta (β). Then the condition stated above for the validity of the inference form "α, therefore β" amounts to saying that no instance of the proposition form "α and not-β" is true—i.e., that every instance of the proposition form (7) Not both: α and not-β is true—or that line (7), fully spelled out, of course, is a valid proposition form. The study of proposition forms, however, cannot be similarly accommodated under the study of inference forms, and so for reasons of comprehensiveness it is usual to regard formal logic as the study of proposition forms. Because a logician's handling of proposition forms is in many ways analogous to a mathematician's handling of numerical formulas, the systems he constructs are often called calculi.
Much of the work of a logician proceeds at a more abstract level than that of the foregoing discussion. Even a formula such as (3) above, though not referring to any specific subject matter, contains expressions like "every" and "is a," which are thought of as having a definite meaning, and the variables are intended to mark the places for expressions of one particular kind (roughly, common nouns or class names). It is possible, however—and for some purposes it is essential—to study formulas without attaching even this degree of meaningfulness to them. The construction of a system of logic, in fact, involves two distinguishable processes: one consists in setting up a symbolic apparatus—a set of symbols, rules for stringing these together into formulas, and rules for manipulating these formulas; the second consists in attaching certain meanings to these symbols and formulas. If only the former is done, the system is said to be uninterpreted, or purely formal; if the latter is done as well, the system is said to be interpreted. This distinction is important, because systems of logic turn out to have certain properties quite independently of any interpretations that may be placed upon them. An axiomatic system of logic can be taken as an example—i.e., a system in which certain unproved formulas, known as axioms, are taken as starting points, and further formulas (theorems) are proved on the strength of these. As will appear later (see below Axiomatization of PC), the question whether a sequence of formulas in an axiomatic system is a proof or not depends solely on which formulas are taken as axioms and on what the rules are for deriving theorems from axioms, and not at all on what the theorems or axioms mean. Moreover, a given uninterpreted system is in general capable of being interpreted equally well in a number of different ways; hence, in studying an uninterpreted system, one is studying the structure that is common to a variety of interpreted systems. Normally a logician who constructs a purely formal system does have a particular interpretation in mind, and his motive for constructing it is the belief that when this interpretation is given to it, the formulas of the system will be able to express true principles in some field of thought; but, for the above reasons among others, he will usually take care to describe the formulas and state the rules of the system without reference to interpretation and to indicate as a separate matter the interpretation that he has in mind.
Many of the ideas used in the exposition of formal logic, including some that are mentioned above, raise problems that belong to philosophy rather than to logic itself. Examples are: What is the correct analysis of the notion of truth? What is a proposition, and how is it related to the sentence by which it is expressed? Are there some kinds of sound reasoning that are neither deductive nor inductive? Fortunately, it is possible to learn to do formal logic without having satisfactory answers to such questions, just as it is possible to do mathematics without answering questions belonging to the philosophy of mathematics such as: Are numbers real objects or mental constructs?
The propositional calculus
Basic features of PC
The simplest and most basic branch of logic is the propositional calculus, hereafter called PC, so named because it deals only with complete, unanalyzed propositions and certain combinations into which they enter. Various notations for PC are used in the literature. In that used here the symbols employed in PC first comprise variables (for which the letters p, q, r, … are used, with or without numerical subscripts); second, operators (for which the symbols ∼, ·, ∨, ⊃, and ≡ are employed); and third, brackets or parentheses. The rules for constructing formulas are discussed below (see below Formation rules for PC), but the intended interpretations of these symbols—i.e., the meanings to be given to them—are indicated here immediately: the variables are to be viewed as representing unspecified propositions or as marking the places in formulas into which sentences, and only sentences, may be inserted. (This is sometimes expressed by saying that variables range over propositions, or that they take propositions as their values.) Hence they are often called propositional variables. It is assumed that every proposition is either true or false and that no proposition is both true and false. Truth and falsity are said to be the truth values of propositions. The function of an operator is to form a new proposition from one or more given propositions, called the arguments of the operator. The operators ∼, ·, ∨, ⊃, and ≡ correspond respectively to the English expressions "not," "and," "or," "if …, then" (or "implies"), and "is equivalent to," when these are used in the following senses:
- Given a proposition p, then ∼p ("not p") is to count as false when p is true and true when p is false; "∼" (when thus interpreted) is known as the negation sign, and ∼p as the negation of p.
- Given any two propositions p and q, then p · q ("p and q") is to count as true when p and q are both true and as false in all other cases (namely, when p is true and q false, when p is false and q true, and when p and q are both false); p · q is said to be the conjunction of p and q; " · " is known as the conjunction sign, and its arguments (p, q) as conjuncts.
- Given any two propositions p and q, then p ∨ q ("p or q") is to count as false when p and q are both false and true in all other cases; thus it represents the assertion that at least one of p and q is true. P ∨ q is known as the disjunction of p and q; "∨" is the disjunction sign, and its arguments (p, q) are known as disjuncts.
- Given any two propositions p and q, then p ⊃ q ("if p [then] q" or "p [materially] implies q") is to count as false when p is true and q is false and as true in all other cases; hence it has the same meaning as "either not-p or q" or as "not both p and not-q." The symbol "⊃" is known as the (material) implication sign, the first argument as the antecedent, and the second as the consequent; q ⊃ p is known as the converse of p ⊃ q.
- Finally, p ≡ q ("p is [materially] equivalent to q" or "p if and only if q") is to count as true when p and q have the same truth value (i.e., either when both are true or when both are false), and false when they have different truth values; the arguments of "≡" (the [material] equivalence sign) are called equivalents.
Brackets are used to indicate grouping; they make it possible to distinguish, for example, between p · (q ∨ r) ("both p and either-q-or-r") and (p · q) ∨ r ("either both-p-and-q or r"). Precise rules for bracketing are given below.
All PC operators take propositions as their arguments, and the result of applying them is also in each case a proposition. For this reason they are sometimes called proposition-forming operators on propositions or, more briefly, propositional connectives. An operator that, like ∼, requires only a single argument is known as a monadic operator; operators that, like all the others listed, require two arguments are known as dyadic.
All PC operators also have the following important characteristic: given the truth values of the arguments, the truth value of the proposition formed by them and the operator is determined in every case. An operator that has this characteristic is known as a truth-functional operator, and a proposition formed by such an operator is called a truth function of the operator's argument(s). The truth functionality of the PC operators is clearly brought out by summarizing the above account of them in Table 1. In it, "true" is abbreviated by "1" and "false" by "0," and to the left of the vertical line are tabulated all possible combinations of truth values of the operators' arguments. The columns of 1s and 0s under the various truth functions indicate their truth values for each of the cases; these columns are known as the truth tables of the relevant operators. It should be noted that any column of four 1s or 0s or both will specify a dyadic truth-functional operator. Because there are precisely 24 (i.e., 16) ways of forming a string of four symbols each of which is to be either 1 or 0 (1111, 1110, 1101, …, 0000), there are 16 such operators in all; the four that are listed here are only the four most generally useful ones.
Formation rules for PC
In any system of logic it is necessary to specify which sequences of symbols are to count as acceptable formulas—or, as they are usually called, well-formed formulas (wffs). Rules that specify this are called formation rules. From an intuitive point of view, it is desirable that the wffs of PC be just those sequences of PC symbols that, in terms of the interpretation given above, make sense and are unambiguous; and this can be ensured by stipulating that the wffs of PC are to be all those expressions constructed in accordance with the following PC-formation rules, and only these:
- FR1.A variable standing alone is a wff.
- FR2.If α is a wff, so is ∼α.
- FR3.If α and β are wffs, (α · β), (α β), (α ∨ β), (α ⊃ β), and (α ≡ β) are wffs.
In these rules α and β are variables representing arbitrary formulas of PC. They are not themselves symbols of PC but are used in discussing PC. Such variables are known as metalogical variables. It should be noted that the rules, though designed to ensure unambiguous sense for the wffs of PC under the intended interpretation, are themselves stated without any reference to interpretation and in such a way that there is an effective procedure for determining, again without any reference to interpretation, whether any arbitrary string of symbols is a wff or not. (An effective procedure is one that is "mechanical" in nature and can always be relied on to give a definite result in a finite number of steps. The notion of effectiveness plays an important role in formal logic.)
Examples of wffs are: p; ∼q; ∼(p · q)—i.e., "not both p and q"; and [∼p ∨ (q ≡ p)]—i.e., "either not p or else q is equivalent to p."
For greater ease in writing or reading formulas, the formation rules are often relaxed. The following relaxations are common: (1) Brackets enclosing a complete formula may be omitted. (2) The typographical style of brackets may be varied within a formula to make the pairing of brackets more evident to the eye. (3) Conjunctions and disjunctions may be allowed to have more than two arguments—for example, p · (q ⊃ r) · ∼r may be written instead of [p · (q ⊃ r)] · ∼r. (The conjunction p · q · r is then interpreted to mean that p, q, and r are all true, p ∨ q ∨ r to mean that at least one of p, q, and r is true, and so forth.)
Validity in PC
Given the standard interpretation, a wff of PC becomes a sentence, true or false, when all its variables are replaced by actual sentences. Such a wff is therefore a proposition form in the sense explained above and hence is valid if and only if all its instances express true propositions. A wff of which all instances are false is said to be unsatisfiable, and one with some true and some false instances is said to be contingent.
An important problem for any logical system is the decision problem for the class of valid wffs of that system (sometimes simply called the decision problem for the system). This is the problem of finding an effective procedure, in the sense explained in the preceding section, for testing the validity of any wff of the system. Such a procedure is called a decision procedure. For some systems a decision procedure can be found; the decision problem for a system of this sort is then said to be solvable, and the system is said to be a decidable one. For other systems it can be proved that no decision procedure is possible; the decision problem for such a system is then said to be unsolvable, and the system is said to be an undecidable one.
PC is a decidable system. In fact, several decision procedures for it are known. Of these the simplest and most important theoretically (though not always the easiest to apply in practice) is the method of truth tables, which will now be explained briefly. Since all the operators in a wff of PC are truth-functional, in order to discover the truth value of any instance of such a wff, it is unnecessary to consider anything but the truth values of the sentences replacing the variables. In other words, the assignment of a truth value to each of the variables in a wff uniquely determines a truth value for the whole wff. Since there are only two truth values and each wff contains only a finite number of variables, there are only a finite number of truth-value assignments to the variables to be considered (if there are n distinct variables in the wff, there are 2n such assignments); these can easily be systematically tabulated. For each of these assignments the truth tables for the operators then enable one to calculate the resulting truth value of the whole wff; the wff is valid if and only if this truth value is truth in each case. As an example, [(p ⊃ q) · r] ⊃ [(∼r ∨ p) ⊃ q] may be tested for validity. This formula states that "if one proposition implies a second one, and a certain third proposition is true, then if either that third proposition is false or the first is true, the second is true."
The calculation is shown in Table 2. As before, 1 represents truth and 0 falsity. Since the wff contains three variables, there are 23 (i.e., 8) different assignments to the variables to be considered, which therefore generate the eight lines of the table. These assignments are tabulated to the left of the vertical line. The numbers in parentheses at the foot indicate the order in which the steps (from 1 through 6) are to be taken in determining the truth values (1 or 0) to be entered in the table. Thus column 1, falling under the symbol ⊃, sets down the values of p ⊃ q for each assignment, obtained from the columns under p and q by the truth table for ⊃; column 2, for (p ⊃ q) · r, is then obtained by employing the values in column 1 together with those in the column under r by use of the truth table for ·; … until finally column 6, which gives the values for the whole wff, is obtained from columns 2 and 5. This column is called the truth table of the whole wff. Since it consists entirely of 1s, it shows that the wff is true for every assignment given to the variables and is therefore valid. A wff for which the truth table consists entirely of 0s is never satisfied, and a wff for which the truth table contains at least one 1 and at least one 0 is contingent. It follows from the formation rules and from the fact that an initial truth table has been specified for each operator that a truth table can be constructed for any given wff of PC.
Among the more important valid wffs of PC are those of Table 3, all of which can be shown to be valid by a mechanical application of the truth-table method. They can also be seen to express intuitively sound general principles about propositions. For instance, because "not (… or …)" can be rephrased as "neither … nor …," the first De Morgan law can be read as "both p and q if and only if neither not-p nor not-q"; thus it expresses the principle that two propositions are jointly true if and only if neither of them is false. Whenever, as is the case in most of the examples given, a wff of the form α ≡ β is valid, the corresponding wffs α ⊃ β and β ⊃ α are also valid. For instance, because (p · q) ≡ ∼(∼p ∨ ∼q) is valid, so are (p · q) ⊃ ∼(∼p ∨ ∼q) and ∼(∼p ∨ ∼q) ⊃ (p · q).
Moreover, although p ⊃ q does not mean that q can be deduced from p, yet whenever a wff of the form α ⊃ β is valid, the inference form "α, therefore β" is likewise valid. This fact is easily seen from the fact that α ⊃ β means the same as "not both: α and not-β"; for, as was noted above, whenever the latter is a valid proposition form, "α, therefore β" is a valid inference form.
Let α be any wff. If any variable in it is now uniformly replaced by some wff, the resulting wff is called a substitution-instance of α. Thus [p ⊃ (q ∨ ∼r)] ≡ [∼(q ∨ ∼r) ⊃ ∼p] is a substitution-instance of (p ⊃ q) ≡ (∼q ⊃ ∼p), obtained from it by replacing q uniformly by (q ∨ ∼r). It is an important principle that, whenever a wff is valid, so is every substitution-instance of it (the rule of [uniform] substitution).
A further important principle is the rule of substitution of equivalents. Two wffs, α and β, are said to be equivalents when α ≡ β is valid. (The wffs α and β are equivalents if and only if they have identical truth tables.) The rule states that, if any part of a wff is replaced by an equivalent of that part, the resulting wff and the original are also equivalents. Such replacements need not be uniform. The application of this rule is said to make an equivalence transformation.
Interdefinability of operators
The rules that have just been stated would enable the first De Morgan law listed in Table 3 to transform any wff containing any number of occurrences of · into an equivalent wff in which · does not appear at all, but in place of it certain complexes of ∼ and ∨ are used. Similarly, since ∼p ∨ q has the same truth table as p ⊃ q, (p ⊃ q) ≡ (∼p ∨ q) is valid, and any wff containing ⊃ can therefore be transformed into an equivalent wff containing ∼ and ∨ but not ⊃. And, since (p ≡ q) ≡ [(p ⊃ q) · (q ⊃ p)] is valid, any wff containing ≡ can be transformed into an equivalent containing ⊃ and · but not ≡, and thus in turn by the previous steps it can be further transformed into one containing ∼ and ∨ but neither ≡ nor ⊃ nor · . Thus, for every wff of PC there is an equivalent wff, expressing precisely the same truth function, in which the only operators are ∼ and ∨, though the meaning of this wff will usually be much less clear than that of the original.
An alternative way of presenting PC, therefore, is to begin with the operators ∼ and ∨ only and to define the others in terms of these. The operators ∼ and ∨ are then said to be primitive. If "=Df" is used to mean "is defined as," then the relevant definitions can be set down as follows:
(α · β) = Df ∼(∼α ∨ ∼β)
(α ⊃ β) = Df (∼α ∨ β)
(α ≡ β) = Df [(α ⊃ β) · (β ⊃ α)] in which α and β are any wffs of PC. These definitions are not themselves wffs of PC, nor is =Df a symbol of PC; they are metalogical statements about PC, used to introduce the new symbols ·, ⊃, and ≡ into the system. If PC is regarded as a purely uninterpreted system, the expression on the left in a definition is simply a convenient abbreviation of the expression on the right. If, however, PC is thought of as having its standard interpretation, the meanings of ∼ and ∨ will first of all have been stipulated by truth tables, and then the definitions will lay it down that the expression on the left is to be understood as having the same meaning (i.e., the same truth table) as the expression on the right. It is easy to check that the truth tables obtained in this way for ·, ⊃, and ≡ are precisely the ones that were originally stipulated for them.
An alternative to taking ∼ and ∨ as primitive is to take ∼ and · as primitive and to define (α ∨ β) as ∼(∼α · ∼β), to define (α ⊃ β) as ∼(α · ∼β), and to define (α ≡ β) as before. Yet another possibility is to take ∼ and ⊃ as primitive and to define (α ∨ β) as (∼α ⊃ β), (α · β) as ∼(α ⊃ ∼β), and (α ≡ β) as before. In each case, precisely the same wffs that were valid in the original presentation of the system are still valid.
Axiomatization of PC
The basic idea of constructing an axiomatic system is that of choosing certain wffs (known as axioms) as starting points and giving rules for deriving further wffs (known as theorems) from them. Such rules are called transformation rules. Sometimes the word "theorem" is used to cover axioms as well as theorems; the word "thesis" is also used for this purpose.
An axiomatic basis consists of
- 1.A list of primitive symbols, together with any definitions that may be thought convenient,
- 2.A set of formation rules, specifying which sequences of symbols are to count as wffs,
- 3.A list of wffs selected as axioms, and
- 4.A set of (one or more) transformation rules, which enable new wffs (theorems) to be obtained by performing certain specified operations on axioms or previously obtained theorems.
Definitions, where they occur, can function as additional transformation rules, to the effect that, if in any theorem any expression of the form occurring on one side of a definition is replaced by the corresponding expression of the form occurring on the other side, the result is also to count as a theorem. A proof or derivation of a wff α in an axiomatic system S is a sequence of wffs of which the last is α itself and each wff in the sequence is either an axiom of S or is derived from some axiom(s) or some already-derived theorem(s) or both by one of the transformation rules of S. A wff is a theorem of S if and only if there is a proof of it in S.
Care is usually taken, in setting out an axiomatic basis, to avoid all reference to interpretation. It must be possible to tell purely from the construction of a wff whether it is an axiom or not. Moreover, the transformation rules must be so formulated that there is an effective way of telling whether any purported application of them is a correct application or not, and hence whether a purported proof of a theorem really is a proof or not. An axiomatic system will then be a purely formal structure, on which any one of a number of interpretations, or none at all, may be imposed without affecting the question of which wffs are theorems. Normally, however, an axiomatic system is constructed with a certain interpretation in mind; the transformation rules are so formulated that under that interpretation they are validity preserving (i.e., the results of applying them to valid wffs are always themselves valid wffs); and the chosen axioms either are valid wffs or are expressions of principles of which it is desired to explore the consequences.
Probably the best-known axiomatic system for PC is the following one, which, since it is derived from Principia Mathematica (1910–13) by Alfred North Whitehead and Bertrand Russell, is often called PM:
- Primitive symbols: ∼, ∨, (,), and an infinite set of variables, p, q, r, … (with or without numerical subscripts).
- Definitions of ·, ⊃, ≡ (see above Interdefinability of operators).
- Formation rules (see above Formation rules for PC), except that formation rule 3 can be abbreviated to "If α and β are wffs, (α ∨ β) is a wff," since ·, ⊃, and ≡ are not primitive.
- Axioms:
- (p ∨ p) ⊃ p
- q ⊃ (p ∨ q)
- (p ∨ q) ⊃ (q ∨ p)
- (q ⊃ r) ⊃ [(p ∨ q) ⊃ (p ∨ r)]
Axiom 4 can be read, "If q implies r, then, if either p or q, either p or r."
- Transformation rules:
- The result of uniformly replacing any variable in a theorem by any wff is a theorem (rule of substitution).
- If α and (α ⊃ β) are theorems, then β is a theorem (rule of detachment, or modus ponens).
Relative to a given criterion of validity, an axiomatic system is sound if every theorem is valid, and it is complete (or, more specifically, weakly complete) if every valid wff is a theorem. The axiomatic system PM can be shown to be both sound and complete relative to the criterion of validity already given (see above Validity in PC).
An axiomatic system is consistent if, whenever a wff α is a theorem, ∼α is not a theorem. (In terms of the standard interpretation, this means that no pair of theorems can ever be derived one of which is the negation of the other.) It is strongly complete if the addition to it (as an extra axiom) of any wff whatever that is not already a theorem would make the system inconsistent. Finally, an axiom or transformation rule is independent (in a given axiomatic system) if it cannot be derived from the remainder of the axiomatic basis (or—which comes to the same thing—if its omission from the basis would make the derivation of certain theorems impossible). It can, moreover, be shown that PM is consistent and strongly complete and that each of its axioms and transformation rules is independent.
A considerable number of other axiomatic bases for PC, each having all the above properties, are known. The task of proving that they have these properties belongs to metalogic.
In some standard expositions of formal logic, the place of axioms is taken by axiom schemata, which, instead of presenting some particular wff as an axiom, lay it down that any wff of a certain form is an axiom. For example, in place of axiom 1 in PM, one might have the axiom schema "Every wff of the form (α ∨ α) ⊃ α is an axiom"; analogous schemata can be substituted for the other axioms. The number of axioms would then become infinite, but, on the other hand, the rule of substitution would no longer be needed, and modus ponens could be the only transformation rule. This method makes no difference to the theorems that can be derived, but, in some branches of logic (though not in PC), it is simpler to work with axiom schemata rather than with particular axioms and substitution rules. Having an infinite number of axioms causes no trouble provided that there is an effective way of telling whether a wff is an axiom or not.
Special systems of PC
Partial systems of PC
Various propositional calculi have been devised to express a narrower range of truth functions than those of PC as expounded above. Of these, the one that has been most fully studied is the pure implicational calculus (PIC), in which the only operator is ⊃, and the wffs are precisely those wffs of PC that can be built up from variables, ⊃, and brackets alone. Formation rules 2 and 3 (see above Formation rules for PC) are therefore replaced by the rule that if α and β are wffs, (α ⊃ β) is a wff. As in ordinary PC, p ⊃ q is interpreted as "p materially implies q"—i.e., as true except when p is true but q false. The truth-table test of validity can then be straightforwardly applied to wffs of PIC.
The task of axiomatizing PIC is that of finding a set of valid wffs, preferably few in number and relatively simple in structure, from which all other valid wffs of the system can be derived by straightforward transformation rules. The best-known basis, which was formulated in 1930, has the transformation rules of substitution and modus ponens (as in PM) and the following axioms:
- p ⊃ (q ⊃ p)
- [(p ⊃ q) ⊃ p] ⊃ p
- (p ⊃ q) ⊃ [(q ⊃ r) ⊃ (p ⊃ r)]
Axioms 1 and 3 are closely related to axioms 2 and 4 of PM respectively (see above Axiomatization of PC). It can be shown that the basis is complete and that each axiom is independent.
Under the standard interpretation, the above axioms can be thought of as expressing the following principles: (1) "If a proposition p is true, then if some arbitrary proposition q is true, p is (still) true." (2) "If the fact that a certain proposition p implies some arbitrary proposition q implies that p itself is true, then p is (indeed) true." (3) "If one proposition (p) implies a second (q), then if that second proposition implies a third (r), the first implies the third." The completeness of the basis is, however, a formal matter, not dependent on these or any other readings of the formulas.
An even more economical complete basis for PIC contains the same transformation rules but the sole axiom [(p ⊃ q) ⊃ r] ⊃ [(r ⊃ p) ⊃ (s ⊃ p)]. It has been proved that this is the shortest possible single axiom that will give a complete basis for PIC with these transformation rules.
Since PIC contains no negation sign, the previous account of consistency is not significantly applicable to it. Alternative accounts of consistency have, however, been proposed, according to which a system is consistent (1) if no wff consisting of a single variable is a theorem or (2) if not every wff is a theorem. The bases stated are consistent in these senses.
Nonstandard versions of PC
Qualms have sometimes been expressed about the intuitive soundness of some formulas that are valid in "orthodox" PC, and these qualms have led some logicians to construct a number of propositional calculi that deviate in various ways from PC as expounded above.
Underlying ordinary PC is the intuitive idea that every proposition is either true or false, an idea that finds its formal expression in the stipulation that variables shall have two possible values only—namely, 1 and 0. (For this reason the system is often called the two-valued propositional calculus.) This idea has been challenged on various grounds. Following a suggestion made by Aristotle, some logicians have maintained that propositions about those events in the future that may or may not come to pass are neither true nor false but "neuter" in truth value. Aristotle's example, which has received much discussion, is "There will be a sea battle tomorrow." It has also been maintained, by the English philosopher Sir Peter Strawson and others, that, for propositions with subjects that do not have anything actual corresponding to them—such as "The present king of France is wise" (assuming that France has no king) or "All John's children are asleep" (assuming that John has no children)—the question of truth or falsity "does not arise." Another view is that a third truth value (say, "half-truth") ought to be recognized as existing between truth and falsity; thus, it has been advanced that certain familiar states of the weather make the proposition "It is raining" neither definitely true nor definitely false but something in between the two.
The issues raised by the above examples no doubt differ significantly, but they all suggest a threefold rather than a twofold division of propositions and hence the possibility of a logic in which the variables may take any of three values (say 1, 1/2, and 0), with a consequent revision of the standard PC account of validity. Several such three-valued logics have been constructed and investigated; a brief account will be given here of one of them, in which the most natural interpretation of the additional value (1/2) is as "half-true," with 1 and 0 representing truth and falsity as before. The formation rules are as they were for orthodox PC, but the meaning of the operators is extended to cover cases in which at least one argument has the value 1/2 by the five entries in Table 4. (Adopting one of the three values of the first argument, p, given in the leftmost column [1, 1/2, or 0] and, for the dyadic operators, one of the three values of the second, q, in the top row—above the line—one then finds the value of the whole formula by reading across for p and down for q.) It will be seen that these tables, owing to the Polish logician Jan Łukasiewicz, are the same as the ordinary two-valued ones when the arguments have the values 1 and 0. The other values are intended to be intuitively plausible extensions of the principles underlying the two-valued calculus to cover the cases involving half-true arguments. Clearly, these tables enable a person to calculate a determinate value (1, 1/2, or 0) for any wff, given the values assigned to the variables in it; a wff is valid in this calculus if it has the value 1 for every assignment to its variables. Since the values of formulas when the variables are assigned only the values 1 and 0 are the same as in ordinary PC, every wff that is valid in the present calculus is also valid in PC. Some wffs that are valid in PC are, however, now no longer valid. An example is (p ∨ ∼p), which, when p has the value 1/2, also has the value 1/2. This reflects the idea that if one admits the possibility of a proposition's being half-true, one can no longer hold of every proposition without restriction that either it or its negation is true.
Given the truth tables for the operators in Table 4, it is possible to take ∼ and ⊃ as primitive and to define (α ∨ β) as [(α ⊃ β) ⊃ β]—though not as (∼α ⊃ β), as in ordinary PC; (α · β) as ∼(∼α ∨ ∼β); and (α ≡ β) as [(α ⊃ β) · (β ⊃ α)]. With these definitions as given, all valid wffs constructed from variables and ∼, ·, ∨, ⊃, and ≡ can be derived by substitution and modus ponens from the following four axioms:
- p ⊃ (q ⊃ p)
- (p ⊃ q) ⊃ [(q ⊃ r) ⊃ (p ⊃ r)]
- [(p ⊃ ∼p) ⊃ p] ⊃ p
- (∼p ⊃ ∼q) ⊃ (q ⊃ p)
Other three-valued logics can easily be constructed. For example, the above tables might be modified so that ∼1/2, 1/2 ⊃ 0, 1/2 ≡ 0, and 0 ≡ 1/2 all have the value 0 instead of 1/2, as before, leaving everything else unchanged. The same definitions are then still possible, but the list of valid formulas is different; e.g., ∼∼p ⊃ p, which was previously valid, now has the value 1/2 when p has the value 1/2. This system can also be successfully axiomatized. Other calculi with more than three values can also be constructed along analogous lines.
Other nonstandard calculi have been constructed by beginning with an axiomatization instead of a definition of validity. Of these, the best-known is the intuitionistic calculus, devised by Arend Heyting, one of the chief representatives of the intuitionist school of mathematicians, a group of theorists who deny the validity of certain types of proof used in classical mathematics (see mathematics, foundations of: Intuitionistic logic). At least in certain contexts, members of this school regard the demonstration of the falsity of the negation of a proposition (a proof by reductio ad absurdum) as insufficient to establish the truth of the proposition in question. Thus they regard ∼∼p as an inadequate premise from which to deduce p and hence do not accept the validity of the law of double negation in the form ∼∼p ⊃ p. They do, however, regard a demonstration that p is true as showing that the negation of p is false and hence accept p ⊃ ∼∼p as valid. For somewhat similar reasons, these mathematicians also refuse to accept the validity of arguments based on the law of excluded middle (p ∨ ∼p). The intuitionistic calculus aims at presenting in axiomatic form those and only those principles of propositional logic that are accepted as sound in intuitionist mathematics. In this calculus, ∼, ·, ∨, and ⊃ are all primitive; the transformation rules, as before, are substitution and modus ponens; and the axioms are the following:
- p ⊃ (p · p)
- (p · q) ⊃ (q · p)
- (p ⊃ q) ⊃ [(p · r) ⊃ (q· r)]
- [(p ⊃ q) · (q ⊃ r)] ⊃ (p ⊃ r)
- p ⊃ (q ⊃ p)
- [p · (p ⊃ q)] ⊃ q
- p ⊃ (p ∨ q)
- (p ∨ q) ⊃ (q ∨ p)
- [(p ⊃ r) · (q ⊃ r)] ⊃ [(p ∨ q) ⊃ r]
- ∼p ⊃ (p ⊃ q)
- [(p ⊃ q) · (p ⊃ ∼q)] ⊃ ∼p
From this basis neither p ∨ ∼p nor ∼∼p ⊃ p can be derived, though p ⊃ ∼∼p can. In this respect this calculus resembles the second of the three-valued logics described above. It is, however, not possible to give a truth-table account of validity—no matter how many values are used—that will bring out as valid precisely those wffs that are theorems of the intuitionistic calculus and no others.
Natural deduction method in PC
PC is often presented by what is known as the method of natural deduction. Essentially this consists of a set of rules for drawing conclusions from hypotheses (assumptions, premises) represented by wffs of PC and thus for constructing valid inference forms. It also provides a method of deriving from these inference forms valid proposition forms, and in this way it is analogous to the derivation of theorems in an axiomatic system. One such set of rules is presented in Table 5 (and there are various other sets that yield the same results).
A natural deduction proof is a sequence of wffs beginning with one or more wffs as hypotheses; fresh hypotheses may also be added at any point in the course of a proof. The rules may be applied to any wff or group of wffs, as appropriate, that have already occurred in the sequence. In the case of rules 1–7, the conclusion is said to depend on all of those hypotheses that have been used in the series of applications of the rules that have led to this conclusion; i.e., it is claimed simply that the conclusion follows from these hypotheses, not that it holds in its own right. An application of rule 8 or rule 9, however, reduces by one the number of hypotheses on which the conclusion depends; and a hypothesis so eliminated is said to be a discharged hypothesis. In this way a wff may be reached that depends on no hypotheses at all. Such a wff is a theorem of logic. It can be shown that those theorems derivable by the rules stated above—together with the definition of α ≡ β as (α ⊃ β) · (β ⊃ α)—are precisely the valid wffs of PC. A set of natural deduction rules yielding as theorems all the valid wffs of a system is complete (with respect to that system) in a sense obviously analogous to that in which an axiomatic basis was said above to be complete (see Axiomatization of PC.
As an illustration, the formula [(p ⊃ q) · (p ⊃ r)] ⊃ [p ⊃ (q · r)] will be derived as a theorem of logic by the natural deduction method. (The sense of this formula is that, if a proposition [p] implies each of two other propositions [q, r], then it implies their conjunction.) Explanatory comments follow the proof.
The figures in parentheses immediately preceding the wffs are simply for reference. To the right is indicated either that the wff is a hypothesis or that it is derived from the wffs indicated by the rules stated. On the left are noted the hypotheses on which the wff in question depends (either the first or the second line of the derivation, or both). Note that since 8 is derived by conditional proof from hypothesis 2 and from 7, which is itself derived from hypotheses 1 and 2, 8 depends only on hypothesis 1, and hypothesis 2 is discharged. Similarly, 9 depends on no hypotheses and is therefore a theorem.
By varying the above rules it is possible to obtain natural deduction systems corresponding to other versions of PC. For example, if the second part of the double-negation rule is omitted and the rule is added that, given α · ∼α, one may then conclude β, it can be shown that the theorems then derivable are precisely the theorems of the intuitionistic calculus.


text: 8 Aug 2018 0 2018 Kia Stinger-47 by Zeid Nasser 108 Share Previous: Road Test: 2018 Kia Stinger GT2 Related posts About The Author Zeid Nasser There are no comments yet Why not be the first Leave a Reply Cancel reply More posts in category Recommended for you Car Ownership Costs Cars are among the most expensive items that you will purchase in your lifetime. AAA estimates that… The Intelligent Driver Toggle navigation Home News Reviews Auto Shows DIY About Latest Car Ownership Costs May 21, 2019 The Benefits Of Owning A Motorcycle May 21, 2019 Buying A Car: Do You Really Need To Worry About Depreciation? May 8, 2019 Social facebook twitter


text: Semiconductor A semiconductor is a solid whose electrical conductivity can be controlled over a wide range either permanently or dynamically. Semiconductors are tremendously important technologically and economically. Semiconductors are essential materials in all modern electrical devices, from computers to cellular phones to digital audio players. Silicon is the most commercially important semiconductor, though dozens …Read More »


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You know the feeling, that little tingle in your nose or throat, followed by a few sneezes and the feeling that you could take a nap just about anywhere. You are coming down with a cold. Now what do you do to halt its progress and prevent future infections?
Of course NOT catching a cold is the best option and the ultimate in prevention is to simply not come in contact with a cold or flu virus. Chances are you will though. You can improve your odds if you frequently wash your hands, dont touch your eyes, nose, or mouth and try not to hang out with sick people. This of course is easier said than done.
Rhinoviruses account for a majority of cold virus infections in the fall, and of those exposed 70-80% will go on to develop symptoms. The goal once infected is to be in the 20-30% that dont develop symptoms or if you do have symptoms, reduce their duration and severity.
One very cost-effective way to reduce the symptoms of a cold is to have a good attitude and a positive outlook on life. A study published in 2003 in Psychosomatic Medicine found those with positive attitudes had fewer cold symptoms than those with depressed or angry attitudes. Outlook on life did not have an effect on who caught a cold. Happy people became infected at the same rate as those with negative attitudes; they just didnt feel as bad!
Cold viruses appear to take advantage of a weakened immune system. Factors that can weaken the immune system include excess alcohol and sugar consumption, stress, and lack of sleep. A healthy diet, moderate exercise, adequate sleep, and stress control form the foundation for an immune system that will be ready to fend off respiratory viruses.
Key Vitamins and Minerals
Adequate, but not excessive, intakes of vitamins A, C, E, D and B6, zinc, and iron appear to be especially important in maintaining immunity. Most people, and especially those with type 2 diabetes, benefit from a daily multivitamin and mineral supplement. It can help meet the basic nutritional needs of those who are stressed or who dont eat a healthy balanced diet. Make sure your multi includes selenium. According to Dr. Melinda Beck, Ph.D., professor of pediatrics and nutrition at the University of North Carolina at Chapel Hill, a diet lacking adequate amounts of selenium could lead to mutations in the flu virus making it more dangerous. Food sources include Brazil nuts, tuna, chicken, sunflower seeds, garlic and wheat. 55 micrograms per day is the current RDA for adults.
Taking zinc at the very first sign of a cold may help. Studies have found adults taking zinc lozenges containing 9-24 mg elemental zinc gluconate or acetate every 2 hours at the first sign of a cold can significantly decrease the length and severity of the cold. Do not take zinc lozenges for preventing a cold long term as too much zinc can lead to a copper deficiency.
Vitamin D is quickly becoming the new vitamin C for its role in maintaining a healthy immune system. Vitamin D produces cathelicidin and defensins which are proteins with anti-viral effects. It also has anti-inflammatory properties. A 2009 study published in the Archives of Internal Medicine found those with the lowest levels of vitamin D were 36% more likely to have had a respiratory illness than those with the highest levels of vitamin D. Those with asthma or COPD were at an even greater risk. A study published in May 2010 in the American Journal of Clinical Nutrition found that school children receiving 1200 IU of vitamin D a day had a reduced risk of influenza type A compared to those receiving a placebo. Some studies have not found a protective effect with vitamin D however.
The American Academy of Pediatrics recommends all children receive 400 IU/day of vitamin D3 starting in the first few days of life. This is double previous recommendations. Some health experts recommend even higher doses during the winter months. Children under one may take up to 1000 IU/day and children over one may take up to 2000 IU/day, especially during the winter months with low sun exposure. The upper limit is set at 4000 IU/day for adults but your healthcare provider may recommend higher amounts based on individual risk or based on vitamin D testing with a 25(OH) D test. Very high doses of supplemental vitamin D can be toxic.
Phytonutrient-rich Diet
Eat a variety of phytochemical-rich fruits and vegetables. Aim for at least 2-3 servings of fruits and 3-5 servings of vegetables every day. Phytochemicals include a variety of special plant compounds that act in various ways to help support the immune system. Fruits and vegetables with deep or bright colors are especially rich in phytochemicals. Sweet potatoes, kale, blueberries and cherries are a few examples.
Now is the time to kick up the flavor with a variety of spices. Garlic, ginger, and turmeric are common spices with immune boosting and anti-viral properties. Mushrooms are another super-food when it comes to immunity. Maitake and shiitake mushrooms are rich in beta-glucans which are potent immune stimulators.
Consume probiotic-rich foods regularly such as yogurt and kefir. Probiotics help maintain balance in the GI tract by warding off unwanted bacteria and yeast, and recent studies suggest that probiotics can help reduce the length and severity of cold symptoms.
Natural Support
Echinacea is a popular herb that appears to help boost activity of immune cells responsible for fighting all kinds of infections. The use of echinacea for longer than six to eight weeks is not recommended however, as it appears to lose effectiveness. Therefore, you shouldnt take echinacea throughout the entire cold and flu season. Take it only if you have been exposed or feel symptoms coming on. Additionally, the effectiveness of echinacea in studies has been mixed, but the best evidence appears to be when the Echinacea purpurea species is used.
The elderberry, which is a dark purple to black colored berry, seems to hold great potential for those unlucky enough to come down with the flu. Some studies have found that elderberry extract can help reduce the severity of symptoms and duration of the flu by more than 50%. It contains a variety of plant phytochemicals that possess anti-inflammatory and immune stimulating properties. It also appears to help block the virus from replicating and entering cells.


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Getting a CAPI element to perform an action is done by specifying a callback . This is a function which is performed whenever you change the state of a CAPI element. It calls a piece of code whenever a choice is made in a window.
Note that the result of the callback function is ignored, and that its usefulness is in its side-effects.
(make-instance 'push-button
:data "Hello"
#'(lambda (&rest args)
"Hello World")))
(contain *)
Figure 2.3 Specifying a callback
A dialog appears containing the message "Hello World".
Figure 2.4 A dialog displayed by a callback.
The CAPI provides the function
to allow you to pop up a dialog box containing a message and a Confirm button. This is one of many pre-defined facilities that the CAPI offers.
Note: When developing applications in the CAPI, note that your CAPI application windows are run in the same Window system event loop as the Common LispWorks environment itself. This - and the fact that in Common Lisp, user code exists in the same global namespace as the Common Lisp implementation itself - means that a CAPI application running under the Common LispWorks environment can modify the same values as you can concurrently modify from one of the environment's programming tools.
For example, your CAPI application might have a button that, when pressed, sets a slot in a particular object that you could also set by hand in the listener. This situation can lead to unexpected values and behavior in your CAPI application, which may seem to reveal bugs in the application or the Common Lisp product that do not in fact exist.


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Hailing from Valencia, Spain, Vinz Feel Free's large scale wheat paste street art installations where nude women's heads are replaced with bird heads and the heads of business men are altered to look like reptiles.
"Birds and naked people are extracted from the book of Genesis in the Bible. Mayas, Aztechs, Sumerians etc. talk about the figure of reptile as the animals which take control over us, like police in our world. And the frog appears in Apocalypse scenes and is responsible for Humanity disasters. This is why I use them to build men in suit characters." (via)


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With its generous 23-cup capacity, this innovative water-filtration system keeps pure, filtered drinking water conveniently accessible--its sleek, space-saving design fits neatly on the counter or on a shelf in the refrigerator. Functioning as both a water filter and a handy dispenser, the unit comes equipped with a push-button spout for simple one-handed dispensing into a glass, water bottle, or other beverage container, or even into a pot for cooking. Sleek, slim design.
Unlike conventional two-stage carbon filters, the dispenser's next-generation filtration system combines five levels of water-purifying technology. First, its activated carbon and oxidation reduction alloy removes the chlorine taste typically associated with tap water. Next, its Ion Exchange stage removes virtually all dissolved solids that may be left over from public water systems or even leached into water from aluminum, lead, and other types of piping. Finally, three additional stages of filtration remove other impurities and ensure the water receives the appropriate amount of treatment time to deliver a '000' reading on the included laboratory-grade Total Dissolved Solids (TDS) water-testing meter. Thoughtfully designed, the water dispenser also provides a built-in TDS meter holder, a flip-up lid for easily adding more water, and a shape that completely dispenses all the water inside, which means no stale water to worry about. A useful addition to any busy and health-conscious household, the 23-cup water-filtration dispenser measures approximately 6-inches by 11-1/5-inches by 15-1/5-inches and carries a 90-day limited warranty.
Even if you live in a municipality that cleans or treats water, water can pick up chemicals on its way from the treatment plant to your faucet, giving your tap water a metallic or chlorinated taste. ZeroWater's first layer of filtration, activated carbon and oxidation reduction alloy removes the chlorine taste you are accustom to with tap water. The Ion Exchange stage removes virtually all dissolved solids that may be left over from public water systems or even leached into your water from piping such as Aluminum, Lead, Zinc, Nitrate and more. Three additional stages are included to remove other impurities and to ensure your water receives the appropriate amount of treatment time to deliver a '000' reading on your laboratory-grade TDS meter (included). TDS stands for Total Dissolved Solids and represents the amount of dissolved substances that can negatively affect the way water tastes.
Five-Stage Filtration System:
Unlike conventional gravity-fed or carbon water filters that remove only certain substances from your water, ZeroWater's patented 5-stage Ion Exchange System delivers the only filtered water to measure 000 PPM (parts per million) on the TDS meter. Compare that to the levels you'll find in other filtered waters, most bottled waters and plain unfiltered tap water, all of which contain measureable amounts of dissolved solids. TDS meter readings for tap water in the US average between 190 and 200 PPM. Conventional filtered water measures between 030-500 PPM, and bottled water between 000-350 PPM.
Stage 1: Activated carbon infused micro cloth.
Stage 2: Multi-layer system using carbon and oxidation reduces alloy.
Stage 3: Distributor that maximizes contact time.
Stage 4: Comprehensive ION Exchange array.
Stage 5: Non-woven membrane to remove fine particles.
The included TDS meter ensures that you're getting the best-tasting water possible.
Battery-Powered TDS Meter Makes it Easy to Test Your Water:
The beauty of the ZeroWater Pitcher is that you don't have to accept purity claims at face value. Test your water yourself with the included meter and watch as the zeros come together to ensure that you're getting the best-tasting water possible. Powered by two easy-to-replace 1.5-volt button cell batteries (included), this meter also lets you know the status of your filter. For instance, if your meter reads '006', it's time to replace the filter.
* 23-cup container--largest refrigerator filter dispenser available.
* On-hand pull & pour button spout.
* Easy-access fill--refill your dispenser while in the fridge.
* Completely dispenses all water.
* Convenient, space-saving design.
* Built-in TDS meter holder.
* Patented 5-stage dual ion exchange filter--removes virtually all dissolved solids in your water.
In the box:
* 23-cup dispenser
* TDS (total dissolved solids) meter
* ZeroWater Ion Exchange water filter
* User Manual
* Coupons for future filter purchases


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Acrylic Gesso
by Golden
White gesso is a white priming ground to be used on a variety of absorbent surfaces where acrylic colors, polymers, oil colors, tempera or casein will be applied. Black gesso is useful for applications where dark priming is desirable.
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Author Notes: Though I love planning holidays, I still forget things to pack. This time, I remembered the salt, sugar, tomato ketchup, my homemade pancake mix – a blend of flour, ground oats, bran, cinnamon and maple flakes, orange tea and hagelslag. I forgot the rice, the pasta, noodles and everything else in between. We arrived Barcelona hungry and I berated myself.
Right across from our holiday apartment, there is a store. We go in and I head for the carbohydrate aisle, past the beans and rice and straight for the quick cook pasta. J picks up a pack of broken spaghettini and I make that two. Once we know what dinner is made off, we think about the sauce. We spot some sardines, in search of corned beef and tuna. I grab a tin of aceituna neguila – black olives, a bottle of smooth tomato sauce, a jar of preserved red piquillo peppers, 2 onion bulbs, some garlic, vegetable oil, bacon bits and Leon's chorizo. French bread, regular bread, eggs and milk; cans of coca cola, fanta and a large bottle of agua later, we're done. Ready to make our first family dinner in Spain.
Back in the kitchen, I bang pots about and the end result is something like this - a delicious sauce that has us hankering for more - every single one of us! Fingers are licked. Plates wiped clean and a personal reminder to myself - pack right. —Kitchen Butterfly
Food52 Review: This is a quick, smart, and surprisingly complex Spanish pantry sauce that would do any pound of pasta very proud. If you're like me and embrace the chicken of the sea, then you'll want to increase the tuna by another can and maybe even throw in a few anchovies when you're sizzling your tuna oil. It's spicey and rich and the bacon and tomato combo is, as you would expect, delectable. —favabean
Makes: a whole pot
Prep time: 20 min
Cook time: 30 min
1 medium sized onion, peeled and chopped
125 g bacon bits (or more to taste)
3 cloves of garlic, thinly sliced
100g chorizo, chopped
200g piquillo (roasted red pepper) strips or roasted red peppers, cut into 1/2-inch strips
800g smooth tomato sauce
Salt and freshly ground pepper to taste
Pepperoncini Mancinati or cayenne pepper to taste
1 teaspoon of dried oregano or mixed Greek herbs
To serve, fresh & crusty bread for dipping, sliced black olives, freshly cooked spaghettini and torn basil leaves
2 '170g' tins of Tuna in olive/sunflower oil
- Set out a heavy bottomed saucepan and add 2 tablespoons of the tuna oil from the tin to the pan. Let heat up gently on low - medium heat. Add the onions, a pinch of salt and sweat for about 4 - 5 minutes, stirring till softened. Add the bacon bits, stirring all the while. After 2 -3 minutes, add the garlic slices and let cook for a minute.
- Into the pan, add the chopped chorizo and piquillo strips. Stir for a few minutes and then add the tomato sauce, tuna flakes and dried herbs. Season to taste and stir well. Set to simmer for 15 minutes, stirring and ensuring the bits at the bottom are moved about.
- Adjust seasoning and your 'hot' sauce is ready. Enjoy.
- This recipe is a Community Pick!


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Fresh from last week's release of a new iOS app, a move CEO Mark Zuckerberg stated was unequivocally about speeding up the user experience, Facebook is apparently turning its attention to its Android app. Business Insider writes that "a handful of ex-Facebookers and others familiar with Facebook's plans" report being strongly encouraged and, in some cases, forced to use Android devices instead of their iPhones.
It seems like Facebook's management hopes to subject its own employees to the inadequacies their Android users feel on a daily basis, though it's unclear whether Facebook employees were forced to make the change because of the sub par Facebook app, or because of their reluctance to give up their iPhones. Frankly, the former wouldn't necessarily come as a shock: Users of Facebook's Android app have voiced their disappointment for some time, and it can't even begin to compete with the refreshed iPhone app. The pitiful 3.6 out of five stars rating on Google Play also indicates there's significant room for improvement. Just take a look at some of the user reviews.
Facebook's refocus on the UX of its entire base of users is a welcome sight to behold. The move also strongly suggests that Facebook is taking its stockholders' concerns seriously as well, taking efforts to make the mobile experience a pleasurable one so that its forays into advertising on phones and tablets are an easier pill to swallow for its users. We can only hope this translates to a win for loyal Facebook users and brave (if anxious) Facebook stockholders.
Really it would seem that the only parties to suffer in any of this are the Facebook employees forced to eat their own dog food — in the form of the currently lacking Android app. But if it's for the good of the users, then so be it; and given the overwhelming positive reaction to the new iPhone app (something Facebook rarely experience with any update), it's well worth the sacrifice.
Now, onto Windows phone…


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By Mark Cooper
Title: California Superior Court Records, 1847-1983
Creator: California. Superior Court (Sonoma County)
Extent: 360.0 Volumes
Arrangement: Chronological
Judgments in Superior Court in criminal and Civil cases.
Access Restrictions: In many cases, further details on individual volumes can be learned by calling staff at the Sonoma County History and Genealogy Library. To see these materials, please call staff (707/545-0831, ext. 562) to request they be brought from the Archives to the Library
Use Restrictions: No restrictions
Preferred Citation: California Superior Court Records, 1847-1983. Sonoma County History and Genealogy Library, Santa Rosa, CA.
Processing Information: Data extracted from SCL marc records.


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by Andrew Gahwiler, sports information student assistant
VALDOSTA, Ga. - The No. 12 Georgia College golf team finished the first two rounds of the 2013 First Federal Southeastern Collegiate in fourth place with a total two-round score of 592 (plus-16).
The Bobcats finished the first round with a score of 294 and added a second-round score of 298 at the par-72, 7,140-yard Kinderlou Forest Golf Club in Valdosta, Ga.
The Bobcats were led by senior All-American Taylor Smith (Mansfield, Ga.), who followed an even par first round with a one-over 73, good for 10th. Smith carded a pair of birdies today on the par-five 11th.
Classmate and two-time All-American Patrick Garrett (Kennesaw, Ga.) shot a 71 and 75 for a two-over 146 in 12th. Garrett had an up-and-down second round, balancing four birdies with six holes carded over par.
Leading the Southeastern Collegiate is No. 5 Florida Southern College with a two-round total of 575. Second place stands at a tie with No. 2 Barry University and No. 10 Columbus State University sharing a score of 584.
Junior Bryan Fox (Roswell, Ga.) is third for the Bobcats and 26th overall at plus-six after posting a pair of 75s. Sophomore All-American Ryan Trocchio (Norcross, Ga.) and junior Victor Monte (Chantilly, Va.) both sit eight over par at 152. Trocchio shaved two strokes off an opening-round 77, while Monte scored a pair of 76s.
GC golf will play the third and final round of the tournament tomorrow, March 11. Monte is set to tee off with golfers from host Valdosta State University and No. 4 University of North Alabama at 9:20 a.m. on hole No. 1.
The Georgia College Department of Athletics, two-time winners of the PBC Commissioner's Cup, sponsors 11 varsity athletic programs at the NCAA Division II level. As a Division II program, Bobcat Athletics prides itself on balancing the life of the student-athlete, evidenced by the teams' multiple appearances in post-season competition as well as documented academic success and community-service involvement. Sign up at www.twitter.com/BobcatSports and www.facebook.com/gcbobcats for up-to-the-minute reports, and visit www.GCBobcats.com for more information, and to nominate your favorite former Bobcats and Colonials to the GC Athletics Hall of Fame.


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- Parent Category: News
WCHS Inspiration Award Recipients recognized this week; Watseka Homecoming
The 2013 Watseka Community High School Inspiration Award recipients are being honored this week. The 103rd Annual WCHS Alumni Reunion and Banquet is Saturday, September 14th.
The 2013 honorees include: Athletic winners Victor Sampson, Bruce Sullivan, and the 1962-63 Men's Warrior "Sweet 16" Basketball Team. The Academic recipient is David Bergstrom.
The awards will be given out during the 103rd Annual WCHS Alumni Reunion and Banquet Saturday. The honorees will also be recognized during the Homecoming Football game Friday evening when the Warriors host St Thomas More.


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Celebrate your Westfield State Owls fandom with this 6-Pack Kooler tote! Westfield State Owls fans like you know that the only thing better than watching your favorite team in action is watching them while you're enjoying a few of your favorite drinks. This tote, which features a convenient carry handle and an adjustable shoulder strap, makes it easy to kick back and relax before the Westfield State Owls add another win to their record!
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Story highlights
- Google announced the winners of its second annual science fair Monday
- Grand prize winner is teen whose project improves accuracy of breast-cancer diagnoses
- The contest was free and open to all students around the world between 13 and 18
Brittany Wenger learned about artificial intelligence during a seventh-grade school project. She was immediately enthralled, bought a book on programming and taught herself how to code.
Now 17, Wenger won the grand prize at the second annual Google Science Fair on Monday for her project on improving breast cancer diagnosis accuracy using artificial neural networks.
That combination of drive, passion for science and a desire to do something good was common at this year's event. Organizers of the online science fair received thousands of entries from 100 countries, including India, Ukraine, Malta and Swaziland. Google picked 15 finalists and, at a final gala in an airplane hangar in Palo Alto, announced the winners in three age categories, along with a grand-prize winner.
Jonah Kohn, 14, won first place in his age group for a project that helps people with hearing loss experience music through vibrations. A team of three 15- and 16-year-olds from Spain took home a trophy (made entirely out of Legos) for their look at the microscopic creatures that thrive in fresh water.
Two 15-year-old young men from Swaziland researched hydroponic techniques to help subsistence farmers in their homeland, where food shortages are a devastating problem. They won the Science in Action award, which highlighted a project making a practical difference.
Before the winners were announced, the finalists presented their projects one last time on the Google campus Monday afternoon. Groups of young kids from summer camps filed through to meet the young scientists and watch their demonstrations. Some Google employees even brought their children to work for the day just to see the event.
In classic Silicon Valley fashion, many adults were there grilling presenters, just like they would any entrepreneur with a pitch. They asked tough questions about methodology, costs and results. Some even asked about business plans.
One man urged finalist Rohit Fenn to make his eco-friendly toilet design, the Vacu-flush, open source. Fenn's prototype uses a vacuum system that consumes 50% less water than traditional toilets. Unfortunately, his design is still too cost-prohibitive to be made made without the help of established toilet manufacturers.
"They would need to take me seriously, which they won't because I'm 16 years old," he said.
The contest was free to enter and open to all students around the world between 13 and 18 years of age. Google collected entries from January to April and announced the finalists in May. The grand prize winner receives a $50,000 scholarship, an internship and a trip to the Galapagos Islands.
For Wenger, one of the highlights of the experience was meeting famed computer scientist Vint Cerf, who talked with her at length about computer science and neural networks.
For her winning project, Wenger wrote a program that improves diagnoses of malignant breast tumors by using a large amount of data stored online and looking for patterns. It's an ambitious project that was made possible by that first spark of interest in programming five years ago
"I decided that it was what I was going to do," said the Florida native. "I'm very persistent, and I learned to code, and I started coding neural networks that played soccer -- I'm an avid soccer player as well."