Language

A suitable medium for expressive sentences for an agent. A primitive vocabulary and grammatical rules which say which strings of symbols count as well-formed formulas (wffs).

Languages are often misleadingly named.

For example, Propositional Logic, or propositional languages, are sometimes contrasted with Predicate Logic, or First Order Languages, but in fact, both contain both propositions and predicates.

The word calculus has no special meaning, referring to calculation, but, often implies a relatively high level of abstraction or procedural complexity.

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Specific Languages

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Propositional Logic

- a simple knowledge representation language




Disjunctive Normal Form - DNF
Conjunctive Normal Form - CNF

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First Order Logic

Also known as: FOL, first-intentional logic, first order predicate calculus

Contains quantification, but only of concrete individuals.

There have been attempts to demonstrate that FOL is superior to other types of logic.

W.Hodges writes in his Logic ('77,Penguin,p.210) "Curiously there is a flourishing branch of mathematics-called abstract model theory- which is largely devoted to explaining why first order predicate logic works so much better than any other kind of formal logic which has been proposed."

Sowa(2000) on "Status of FOL" p41-42 describes the supporters of the theory of the primacy of first order logic, including W.V Quine and John McCarthy.

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Second Order Logic and beyond

Also known as Higher Order Logic, Second Order Logic,

Contains qualification, which is not limited to concrete individuals, can include relations and propositions.

Modal Logics