derivations

2013

Skills to be acquired in this tutorial:

a) Understanding the nature of derivation. b) Learning elementary Tactics.

Why this is useful:

Tactics will help you to do derivations.

The Tutorial:

a)

A derivation or proof consists of a finite list of lines.

Each line in the list, if understood appropriately, represents something valid. In particular, the last line in the list depicts the argument or theorem under consideration and it is valid. So the derivation amounts to a proof of the validity of the argument or of a theorem.

Tutorial 5. Valid arguments, searching for a proof.

2013

Skills to be acquired in this tutorial:

Proving an argument to be valid by displaying a derivation. Simple propositional derivations using some of the Rules of Inference.

The Tutorial:

If you suspect that an symbolized argument might be valid, you should attempt to give a derivation of it.

A derivation is a proof of validity.

We will do a few derivations first, then, in the next Tutorial, explain in more detail what derivations are and how derivations do the work they should.

7/5/12

Welcome!

These web pages provide an introduction to logic to the level of Propositional and Predicate Calculus.

The focus of the program is on arguments and the question of whether they are valid. Arguments have the form <list of premises> ∴<conclusion>. An argument is valid if and only if it is not possible for all its premises to be true and its conclusion false at one and the same time; an argument which is not valid is invalid.

Roll your own derivations

6/21/07 10 Software

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'. [Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]

You will need to use the correct logical symbols. Here they are

F ∴ F & G ∼ & ∨ ⊃ ≡  ∃ ∴ (or use the palette to produce them)

2/5/08

The Rule of Universal Instantiation UI

If a derivation contains a line of the form

n (<variable>)<scope> <any justification>

then a line of the form

<<scope>[<term>/<variable>]> 'n UI'

may be added to the derivation, provided that <variable> is free for <term> in the <scope> ie that the substitution [<term>/<variable>] is legitimate .

2/5/08 10Software

Reading

Hausman[2007] Logic and Philosophy Chapter 9

The Tutorial

Existential Instantiation permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective.

The circumstance that Existential Instantiation gets invoked looks like this.

2/5/08 10Software

Reading

Hausman[2007] Logic and Philosophy Chapter 9

The Tutorial

There is a rule for adding a Existential Quantifier. This permits the step illustrated by the following proof fragments.

5	Fa
6	(∃x)Fx	5 EG

 

Tutorial 19 Simplified Universal Generalization.

2/5/08 10Software

Reading

Hausman[2007] Logic and Philosophy Chapter 9

The Tutorial

There also is a rule for adding a Universal Quantifier. This permits the step illustrated by the following proof fragments.