Tutorial 21: Existential Elimination

Logical System



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.

Help with the semantics of free variables


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 14: Some Terminology for the Semantics of Predicate Logic

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}

Review of New Material

Logical System

Review of new material

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.