# predicate

## Tutorial 21: Existential Elimination

Topic
Logical System

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.

## Tutorial 20: Existential Introduction

Topic
Logical System

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.

## Tutorial 19: Universal Introduction

Topic
Logical System

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

## Tutorial 18: Universal Elimination

Topic
Logical System

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.

## Help with the semantics of free variables

Topic

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).

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## Tutorial 17: The semantics of quantifiers

Topic
Logical System

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}

Topic
Logical System

## 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

## Tutorial 15: Elementary derivations in predicate logic

Topic
Logical System

2013

### The Tutorial

The sentential rules of derivation carry over unchanged into Predicate Logic

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## Tutorial 14: Some Terminology for the Semantics of Predicate Logic

Topic
Logical System

### 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}

## Tutorial 12: Symbolizing sentences using predicate logic (continued)

Topic
Logical System

2013

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