propositional

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)

Review of new material

There are the truth-tables for the connectives...

Negation

F	∼F
True	False
False	True

Conjunction

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.

10/11/26

Skills to be acquired in this tutorial:

To learn how to symbolize arguments, and how to judge whether they might be invalid using truth-table methods.

Why this is useful:

We wish to appraise arguments, to do this we have to symbolize them first. Judging the invalidity of arguments by truth-table methods is not particularly important, but it does help to develop skills involving truth and lists of formulas.

10/11/26

Skills to be acquired in this tutorial:

To learn how compound propositions are true or false depending on the truth or falsity of their component propositions.

There is the idea of setting up a code or convention or dictionary
between atomic propositions and capital letters.

There are compound propositions, each of which has a main connective
which connects its components.

There are five propositional logical connectives:

'∼' which translates back to 'it is not the case that...'

'.' which translates back to '... and ...'

'∨' which translates back to '... or ...'

'⊃' which translates back to 'if... then ...'

10/11/26

Skills to be acquired in this tutorial:

Symbolizing compound propositions. Learning about logical connectives, and the notion of the main connective. Recognizing different constructions in English which have the same underlying logical form. Paraphrasing the English into a standard form.

Why this is useful:

It is the next step in learning how to symbolize. Main connectives are very important-- they are central to symbolization, they are central to the semantics, and they are central to derivations.

10/11/26

Skills to be acquired in this tutorial:

To become familiar with the notions of argument, valid, invalid, premise, and conclusion. To learn how to symbolize atomic propositions.

Tutorial:

The main role of logic is to assess arguments-- to say whether an individual argument is valid or whether it is invalid. In logic, arguments are taken to consist of two components--premises, and a conclusion.

For example,

If it rains, I get wet.
It rains.

Therefore,

I get wet.

This program provides 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.