Rules of Inference 1

# Rules of Inference 1 - Natural Deduction 7.1 2006 Kevin J....

This preview shows pages 1–17. Sign up to view the full content.

Natural Deduction 7.1 © 2006 Kevin J. Browne

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Rules of Inference I Modus Ponens Modus Tollens Disjunctive Syllogism Hypothetical Syllogism
Modus Ponens p q p _________ q

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Modus Tollens p q ~q _________ ~p
Disjunctive Syllogism p v q ~p _________ q

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Hypothetical Syllogism p q q r _________ p r
Solving proofs in natural deduction is based on pattern recognition. Think of it as using the rules to crack a code!

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example One 1. F v (D T) 2. ~F 3. D /T
Example One 1. F v (D T) 2. ~F 3. D /T Using one of the rules find a pattern in these premises. The pattern here is DS.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example One 1. F v (D T) 2. ~F 1. D /T 2. T 1,2 DS So we draw the conclusion from DS on line 4.
Example One 1. F v (D T) 2. ~F D /T T 1,2 DS Now use the rules to find another pattern with what we’ve just derived.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example One 1. F v (D T) 2. ~F 1. D /T 2. T 1,2 DS 3. 3,4 MP Once we reach the final conclusion we’ve solved the proof!
A more involved example 1. ~M v (B v ~T) 2. B W 3. M 4. ~W /~T Here there are several patterns to identify. We need all of them to crack this code! Here’s one: MT Here’s another: DS

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
A more involved example

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/05/2008 for the course PHIL 311 taught by Professor D.c. during the Spring '07 term at University of Louisville.

### Page1 / 17

Rules of Inference 1 - Natural Deduction 7.1 2006 Kevin J....

This preview shows document pages 1 - 17. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online