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Nondeterministic Three-Valued Logic: Isotonic and Guarded Truth-Functions

Peter Päppinghaus and Martin Wirsing
Studia Logica: An International Journal for Symbolic Logic
Vol. 42, No. 1 (1983), pp. 1-22
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015084
Page Count: 22
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Nondeterministic Three-Valued Logic: Isotonic and Guarded Truth-Functions
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Abstract

Nondeterministic programs occurring in recently developed programming languages define nondeterminate partial functions. Formulas (Boolean expressions) of such nondeterministic languages are interpreted by a nonempty subset of {T ("true"), F ("false"), U ("undefined)}. As a semantic basis for the propositional part of a corresponding nondeterministic three-valued logic we study the notion of a truth-function over {T, F, U} which is computable by a nondeterministic evaluation procedure. The main result is that these truth-functions are precisely the functions satisfying four basic properties, called ⊆-isotonic, ⊆⁻-isotonic, hereditarily guarded, and hereditarily guard-using, and that a function satisfies these properties iff it is explicitly definable (in a certain normal form) from "if..then..else..fi", binary choice, and coustants.

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