gentzen

Quiz 7.

10/29/06

Quiz 7 Applet

The later parts of this can be quite difficult, so it is configured in such a way that the bulk of the work and marks are on intermediate level material. [There is a small quantity of the more challenging material to engage the advanced students.]

10Software

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.

The Tutorial

In Predicate Logic there are two new logical connectives, the Universal Quantifier (∀x) and the Existential Quantifier (∃x). These are used for symbolizing certain English constructions (they also have their own rules of inference and their own semantics, which we will learn about later).

2013

The Tutorial

The propositional rules of derivation carry over unchanged into Predicate Logic

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10Software

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}

Introduction to Semantics

12/25/06

Introduction to Semantics

This video illustrates use of the downloadable application (and the symbol ∧ for 'and'). But, what it depicts and explains is equally good if you happen to be using the web pages applets (or a different symbol for 'and' eg '.').

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2013

A start can be made in predicate logic by taking apart 'atomic' propositions 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,

2013

Skills to be acquired in this tutorial:

To start learning how to symbolize propositions using predicate logic.

The Tutorial:

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.

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.