Nondeterministic three-valued logic: Isotonic and guarded truth-functions

Studia Logica 42 (1):1 - 22 (1983)
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 constants.
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DOI 10.1007/BF01418755
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An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
Many-Valued Logic.Nicholas Rescher - 1969 - New York: Mcgraw-Hill.
Mathematical Theory of Computation.Zohar Manna - 1979 - Journal of Symbolic Logic 44 (1):122-124.

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