CMPUT272 Lecture Notes - Lecture 8: Logical Form, Modus Tollens, Universal Instantiation

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September 25 2014
ETLC 2-001
Predicate Logic
Rules of inference for quantified formulas
Valid argument forms
p q
p q
q
To show that this argument form is valid..
It must be impossible for the conclusion to be false given
the premises to be true.
If the presmises are true, the conclusion must be true.
That is, forms a tautology, ((p q) p) q is a ⟹ ⟹
tautology
Remember...
p q
p
q (Modus Pones)
equates
p q
p q∼ ∨
=
p q∼ ∨
p q∴ ⟹
=
(p q) ( p q)∼ ∨⟹ ⟺
Algebraric rules
p q = p q∼ ∨
p q = (p q) ( p q) ∧ ∼
p q = (p q) (q p)⟺ ⟹
Hypothetical Reasoning
p
.
.
q
p q∴ ⟹
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Document Summary

Valid argument forms p q q p q . To show that this argument form is valid It must be impossible for the conclusion to be false given the premises to be true. If the presmises are true, the conclusion must be true. That is, forms a tautology, ((p q) p) q is a. Remember tautology q p p q (modus pones) equates q p p q p q p (p q) q ( p q) Algebraric rules q = p q p q = (p q) ( p q) p p q = (p p) q) (q. 26 p beyond line 32: p (assumption) \ | cannot be used beyond line: q (deduced from inference) , p q (15-25 and application of hypothetical reasoning) | cannot be used: f (deduced from inference) , p, p. Example (premise) q (premise: p q, p want to deduce q, q, p (assumption) (2,3 modus tollens) (1,4 elimination)

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