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

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∴ ⟹

## 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)