derivations

The Tutorial

The propositional rules of derivation carry over unchanged into Predicate Logic

Exercises to accompany Predicate Tutorial 5

Exercise 1 (of 1).

10/12/26

You now have to tools to appraise propositional arguments.

Let us run through how these might be used with two examples.

Example 1.

Consider the argument

If no human action is free, then no one is responsible for what they do.
If no one is responsible for what they do, no one should be punished.
Therefore
If no human action is free, no one should be punished.

First it should be symbolized

10/12/26

Skills to be acquired

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

10/12/26

Skills to be acquired:

Learning conditional proof.

The Tutorial:

There is an additional propositional rule of inference-- Conditional Proof-- which is slightly more difficult than the ones that we have met before. It is slightly more difficult in that it requires you to make new assumptions, and the correct new assumptions at that.

10/12/26

Skills to be acquired in this tutorial:

a) Learning further propositional rules of inference. Carrying out simple propositional derivations using some of the Rules of Inference.

b) Learning elementary Tactics.

Why this is useful:

Tactics will help you to do derivations.

The Tutorial:

a)

10/12/26

Skills to be acquired in this tutorial:

Learning further propositional rules of inference. Carrying out simple propositional derivations using some of the Rules of Inference.

The Tutorial:

Thus far we have encountered 3 propositional rules of inference: Simplification, Conjunction, and Addition. If we write these out as forms or patterns, these are the kinds of inferences they permit.

Simplication (Simp)

p.q 
∴ 
p

Conjunction (Conj)

10/11/26

Skills to be acquired in this tutorial:

Proving an argument to be valid by displaying a derivation. Carrying out 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.

Tutorials 11 to 25: predicate logic, using the Copi syntax.

8/10/2026

It has become a challenge to run the legacy Deriver application, which was written in Java Swing, simply because few Users have Java on their computers. Fortunately, Leaning Technologies have devised some technology, CheerpJ, that allow Java Swing applications to run in a web browser. 

Example of a difficult derivation

6/1/09 [need to check]