{'fraction_non_alphanumeric': 0.03225806451612903, 'fraction_numerical': 0.007121910347716799, 'mean_word_length': 4.768115942028985, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An Intuitive Axiomatic Development of Truth-Functional Logic

In an introductory logic course, little attention is given to the axiomatic development of truth-functional logic. The student is first taught the concept of validity: "in a valid argument, it is not possible for the conclusion to be false when all the premises are true" (McKay 9). With this definition in mind, the student is then taught to construct proofs to show that arguments are valid. She is given a set of rules to manipulate formulas and an explanation of how to construct proofs. How does the student know that she has enough rules to construct proofs for any valid argument? And how does the student know that she can construct proofs only for valid arguments? Not until an intermediate logic class does the student encounter an an swer to these questions. Most authors axiomatically develop a truth-functional logic, setting up a system with a minimum number of axioms and one rule of inference, modus ponens. For example, Irving Copi uses the following three ax ioms and one rule of inference: Axiom 1) p3(p p). Axiom 2) (p-q)3p. Axiom 3) (p3q)3[~(q r)=)-(r p)], and Rule 1) From p and pz)q to infer q (Copi 227-28). While the first two axioms and the rule of inference may be intuitive enough, the third axiom has little intuitive meaning for the beginning logic student. Furthermore, it is not intuitively obvious that these axioms allow the student to use the rules they have been using to construct proofs. Church's system, Gdtlind-Rasiowa's system, Frege's system, and Lukasiewicz's system all have similar unintuitive axioms (Copi 237). In most intermediate logic textbooks, authors prove that their systems are complete and consistent. Then they show that the rules the students have been using all along to construct proofs can be derived as theorems from their axiomatic system. In this paper, we develop an axiomatic system of truth-functional logic which more closely mirrors the actual way students are taught to construct proofs. The axioms are elementary valid arguments which allow for the introduc tion and elimination of the truth-functional operators. The rules of inference are structural rules which allow for the combination of these elementary valid argu ments to prove other arguments are valid. The constructed system conforms to the intuition of a beginning logic student doing proofs.