derivations

Reductio ad Absurdum

2/24/06

Absurd Introduction and Simple Reductio

2013

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).

The Tutorial:

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

9/12/06

Conditional Proof

This video shows the techniques for Conditional Proof using the downloadable application Deriver. But the techniques are exactly the same for the Proof applet running in a web page. So, the video may look slightly different to what you are looking at, but the underlying principles and approach are the same.

2013

Skills to be acquired:

Learning conditional proof.

The Tutorial:

The four remaining propositional 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.

Two of them are classical forms of inference, dating back thousands of years-- we will look at these first.

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.

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.

Or Introduction

Tutorial 5. Valid arguments, searching for a proof.

Under construction 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.

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.