predicate

2013

Reading

Bergmann[2004] The Logic Book Section 10.1.

The Tutorial

Existential Elimination (often called '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.

2013

Reading

Bergmann[2004] The Logic Book Section 10.1.

The Tutorial

There is a rule for adding a Existential Quantifier, Existential Introduction (also commonly known as 'Existential Generalization'). This permits the step illustrated by the following proof fragments.

2013

Skill to be acquired:

To learn the rule for adding a Universal Quantifier.

Reading

Bergmann[2004] The Logic Book Section 10.1.

The Tutorial

There also is a rule for adding a Universal Quantifier (often called 'Universal Generalization'). This permits the step illustrated by the following proof fragments.

The rule is

The Rule of Universal Introduction UI

If a derivation contains a line of the form

2013

Skill to be acquired:

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

Reading

Bergmann[2004] The Logic Book Section 10.1.

12/25/06

Introduction to Free Variables

This video illustrates use of the downloadable application (and the symbol ∧ for 'and' and (∀x) for the universal quantifier, some systems use (x) for this). But, what the film depicts and explains is equally good if you happen to be using the web pages applets (or different symbols for 'and' and the universal quantifier).

2013

The Tutorial

We will certainly wish to discuss the truth and falsity of formulas with quantifiers in them.

Let us start with an Interpretation

Interpretation 1

Universe= {a,b}
F={a}

Tutorial 16 Symbolization using the quantifiers.

2013

Skill to be acquired in this tutorial:

To learn how to use the Universal and Existential Quantifiers in symbolizing propositions.

Reading

Bergmann[2008] The Logic Book Sections 7.4

2013

The Tutorial

The sentential rules of derivation carry over unchanged into Predicate Logic

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1/10/20

The Tutorial

A few concepts are needed give a simple portrayal of the truth and falsity of predicate logic formulas.

There is the notion of an Interpretation which consists of a Universe together with an account of how the various symbols in the predicate logic formulas apply in this Universe.

There should be a Universe, which is the collection of the objects that the formulas is about. We write, for example,

Universe = {a,b,c}

2013

In predicate logic, many different styles of expression in English get cast into the same 'property-is-had-by-entity' form. For example,