gentzen

11/30/06

[The core of this is from Leblanc and Wisdom [1972] p.117 and f.]

Symbolization using the Universal Quantifier (of non relational English)

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.

8/11/2026

The Tutorial

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

8/12/26

The Tutorial

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

8/12/26

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 Invalidity

10/30/06 Quiz 7 was formerly known as Quiz 4

Quiz 7 Invalidity

[This has been done in the downloadable application, but the principles apply to the applet version also.]

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.]