derivations

6/2/09

Negation Introduction, Simple Reductio

Advanced Reductio via Negation Elimination

6/2/09 10Software

Skills to be acquired:

Learning the Rules Or Elimination and the Introduction of the Biconditional.

Reading

Bergmann[2008] The Logic Book Section 5.1 and 5.4

The Tutorial:

Or Elimination, in the guise of Dilemma, also is a form of inference dating from antiquity.

3/16/06

So that we can show certain arguments to be valid.

The focus of the course lies with the validity and invalidity of arguments. Now, invalidity can be established by counter-example (by producing an interpretation under which all the premises are true and the conclusion false, at the same time). But validity is a different matter. And the usual approach is to have rules of inference and to do derivations.

6/2/09 10 Software

Skills to be acquired:

Learning reductio proof, both as plain Negation Introduction and via (double) Negation Elimination (to prove some formulas that do not have negation as their main connective).

Reading

Bergmann[2004] The Logic Book Section 5.1 and 5.4

The Tutorial:

Reductio ad Absurdum is the second of the classical forms of inference.

6/1/09

Conditional Proof

6/1/09 10 Software

Skills to be acquired:

Learning conditional proof.

Reading

Bergmann[2008] The Logic Book Section 5.1 and 5.4

The Tutorial:

The five remaining core sentential rules of inference are slightly more difficult than the ones that we have met before. They are slightly more difficult in that they require you to make new assumptions, and the correct new assumptions at that. However they follow a similar pattern to each other so mastery of one should lead to mastery of the others.

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.

5/29/09 10Software

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.

Reading

Bergmann[2008] The Logic Book Section 5.1 and 5.4.

The Tutorial:

a)

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

Or Introduction