E. W. Beth

Evert Willem Beth (July 7, 1908 – April 12, 1964) was a Dutch philosopher and logician, whose work principally concerned the foundations of mathematics.

Contributions to Logic

Definition Theorem

The Definition Theorem states that a predicate (or function or constant) is implicitly definable if and only if it is explicitly definable.

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Semantic Tableaux

A proof method for formal systems; cf. Gentzen's natural deduction and sequent calculus, or even Abraham Robinson's resolution and Hilbert's axiomatic systems). It is considered by many to be intuitively simple, particularly for students not acquainted with the study of logic (Wilfred Hodges for example presents semantic tableaux in his introductory textbook, Logic, and Melvin Fitting does the same in his presentation of first-order logic for computer scientists, First-order logic and automated theorem proving).

Related Topics:
Gentzen - Natural deduction - Sequent calculus - Abraham Robinson - Resolution - Hilbert's - Wilfred Hodges - Melvin Fitting - Computer scientists

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One starts out with the intention of proving that a certain set Gamma of formulae imply another formula phi , given a set of rules determined by the semantics of the formulae's connectives (and quantifiers, in First-order logic). The method is to assume the concurrent truth of every member of Gamma and of eg phi (the negation of phi ), and then to apply the rules to branch this list into a tree-like structure of (simpler) formulae until every possible branch contains a contradiction. At this point it will have been established that Gamma cup { eg phi } is inconsistent, and thus that the formulae of Gamma together imply phi .

Related Topics:
Connectives - First-order logic

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Beth Models

A class of models for non-classical logic (cf. Kripke semantics).

Related Topics:
Non-classical logic - Kripke semantics

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