derivations

4/24/06

Tutorial 25 Exercises d

4/24/06

9/13/20

Skill to be acquired:

To understand the concepts of scope, free, bound, and free for.

Why this is useful:

The new predicate rules of inference using quantifiers have restrictions on them which are expressed in terms of these concepts.

10/29/06 Applet removed 2013

Quiz 8 Applet

This contains an applet, so it will be slow loading and likely it will ask you about security.

2013

The Tutorial

Existential Instantiation permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective. It is one of those rules which involves the adoption and dropping of an extra assumption (like ∼I,⊃I,∨E, and ≡I).

The circumstance that Existential Instantiation gets invoked looks like this.

8/11/2026

The Tutorial

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

8/12/26

The Tutorial

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

 

8/12/26

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.