Fixpoint semantics for logic programming a survey

The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close para...

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Bibliographic Details
Published in:Theoretical computer science Vol. 278; no. 1; pp. 25 - 51
Main Author: Fitting, Melvin
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 06.05.2002
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Programming theory
Theoretical computing
Fix point
Stability
Semantics
Belnap logic
Valuation
Apt-van Emden Kowalski semantics
Models
Logical programming
Syntax
Stable model semantics
Lattice
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies.
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ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(00)00330-3