derivations

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.

Roll your own derivations

2013

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

And the right syntax (the premises separated by commas and then a 'therefore' followed by the conclusion).

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'.

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2013

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

Example of a Harder Propositional Proof

2/27/06

Example

2013

Skills to be acquired:

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

The Tutorial:

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

The core idea of it that if a conclusion follows from both disjuncts of a disjunction, then the conclusion follows full stop. As an example in English, if either I am going to eat an ice-cream or I am going to eat some cake, and if I eat ice-cream I break my diet, and if I eat cake I break my diet, then ... I break my diet.

Quiz 6 Applet

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