bergmann

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.

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}

1/12/20

Skill to be acquired:

To learn how to interpret simple predicate logic formulas as being true or false.

Why this is useful:

This helps in proving invalidity by the technique of displaying a counter-example.

Reading

Bergmann[2008] The Logic Book Section 8.1

The Tutorial:

In sentential logic, we just took it that each of the atomic sentences either is true or is false-- we did not look into the structure of the sentences.

Truth can be discussed in more detail in predicate logic.

2013

A start can be made in predicate logic by taking apart 'atomic' sentences and by re-phrasing what they have to say in a 'entity-has-property' way.

The constant terms a,b,c...h are used to denote entities, the predicates A,B,C...Z are used to denote properties that these entities have, and these are put together by writing the predicate first followed by the term, for example Gb.

2013

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