Definite clause programs are canonical (over a suitable domain)

Howard A. Blair; Allen L. Brown

doi:10.1007/BF01531067

Definite clause programs are canonical (over a suitable domain)

Howard A. Blair, Allen L. Brown

Department of Electrical Engineering & Computer Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

For each first-order language L with a nonempty Herbrand universe, we construct an algebra C interpreting the function symbols of L that is a model of the Clark equality theory with language L and is canonical in the sense that for every definite clause program P in the language L, T_P^C ↓ ω is the greatest fixed point of T_P^C. The universe of individuals in C is a quotient of the set of terms of L and is, a fortiori, countable if L is countable. If ℒ contains at least one function symbol of arity at least 2, then the graphs of partial recursive functions on C, suitably defined, are representable in a natural way as individuals in C.

Original language	English (US)
Pages (from-to)	1-19
Number of pages	19
Journal	Annals of Mathematics and Artificial Intelligence
Volume	1
Issue number	1-4
DOIs	https://doi.org/10.1007/BF01531067
State	Published - Sep 1990

Keywords

Clause programs
partial recursive functions
semantics

ASJC Scopus subject areas

Artificial Intelligence
Applied Mathematics

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10.1007/BF01531067

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AB - For each first-order language L with a nonempty Herbrand universe, we construct an algebra C interpreting the function symbols of L that is a model of the Clark equality theory with language L and is canonical in the sense that for every definite clause program P in the language L, TPC ↓ ω is the greatest fixed point of TPC. The universe of individuals in C is a quotient of the set of terms of L and is, a fortiori, countable if L is countable. If ℒ contains at least one function symbol of arity at least 2, then the graphs of partial recursive functions on C, suitably defined, are representable in a natural way as individuals in C.

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Definite clause programs are canonical (over a suitable domain)

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Keywords

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