derivations

10Software

The Tutorial

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

3/4/06 10Software

Skill to be acquired:

To understand the concepts of scope, free, bound. To meet substitution and a simplified version of the rule for removing a Universal Quantifier.

2013

The Tutorial

The propositional rules of derivation carry over unchanged into Predicate Logic

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

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

10/8/26

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

8/12/26

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the lower 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 ∼ ∧ ∨ ⊃ ≡ ∀ ∃ ∴

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.

Replacement or Rewrite Rules

6/21/07

Rewrite Rules

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

8/11/2026

Skills to be acquired

Becoming familiar with common inference patterns and being able to use them via rewrite rules. This helps with assessing ordinary everyday reasoning such as that found in the law, in newspapers, in advertisements, etc.

Example of a Harder Propositional Proof: One of De Morgan's Laws

10/23/06

Example