Statement Logic and Proofs

Statement Logic and Proofs - I Proofs in Statement Logic a...

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I. Proofs in Statement Logic: a. Ex: i. (A.B) ii. (B->(C v D)) iii. ~D iv. :. C v. It can be deduced from (A.B)’s truth that B is true. vi. This means that the antecedent of the second premise is true, and thus the consequent must also be true for the conditional to be true. vii.If the consequent is true, C and D cannot be both false. 1. Furthermore, noting that B -> (C v D), and B is true, (C v D) must be true because this is an instance of Modus Ponens. viii. Now, given that (C v D) MUST be true, and given that ~D is true and thus D is false, it follows that C MUST be true, via the disjunctive syllogism argument form. 1. Thus, the argument is valid. b. (p.q) :. q = “simplification” valid form c. In proofs, valid forms are referred to as inference rules, and are means of deducing steps in a proof. d. Inference rules: i. Modus Ponens ii. Modus Tollens iii. Disjunctive Syllogism 1. p v q, ~p, :. q
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iv. Hypothetical Syllogism 1. p->q, q->r, :. p->r v. Constructive Dilemma 1. p v q, p->r, q->s, :. r v s vi. simplification 1. p.q, :. p vii.Conjunction: 1. p, q, :. p.q viii. Addition: 1. p, :. p v q
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  • Spring '08
  • peterhodges
  • Logic, inference rules, Rue

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