predicate

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.

12/24/13

The Tutorial

The semantics of relations proceeds in much the way one would expect-- the new item that has to be taken account of is the order of the terms (because, for example, Tab is not at all the same thing as Tba -- Arthur being taller than Beryl is not the same as Beryl being taller than Arthur).

Let us start with an Interpretation

Interpretation 1

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

2013

Tutorial 22 Symbolizing Relations.

The Tutorial

Thus far we have considered only 'monadic' predicates-- our atomic formulas consist of a predicate followed by only one term-- for example, Fx. But in English we regularly encounter dyadic predicates or relations. For example, 'Arthur is taller than Bert' cannot be symbolized with the tools we have used so far; what is needed is a relation to represent '...is taller than ...' Txy, say, and then the proposition would be symbolized Tab.

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.

2013

The Tutorial

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

2013

The Tutorial

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

2013

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.

Quiz 7.

10/29/06 [applet removed 2013]

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

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.]