derivations

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.

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 .

There are many valid arguments which cannot be shown to be valid using sentential logic alone. For example,

Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.

12/22/05

Introduction to Tactics

This video is set in the context of the downloadable program, but it applies equally well in the setting of a proof applet. [It is also using a different logical system. However it will convey the principles, The video will be replaced with one suitable for this setting.]

9/4/06

Tutorial 5 Example: Doing a derivation

This movie shows the downloadable application being used, but the manipulations are so similar to those of the web page applet that it really covers both.

This video is also using a different logical system, but it is close enough for now to illustrate the important points. [The video will be revised and replaced.]

2/4/08

Indirect Proof

6/21/07

Rewrite Rules

This video uses '&' as the logical symbol for 'and'.

6/21/07

Rewrite Rules

This video uses '&' as the logical symbol for 'and'.