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Achieving compositionality of the stable model semantics forsmodels programs1

Published online by Cambridge University Press:  01 November 2008

EMILIA OIKARINEN  and
TOMI JANHUNEN
EMILIA OIKARINEN
Affiliation:
Helsinki University of Technology, TKK, Department of Information and Computer Science, P.O. Box 5400, FI-02015 TKK, Finland (e-mail: [email protected], [email protected])
TOMI JANHUNEN
Affiliation:
Helsinki University of Technology, TKK, Department of Information and Computer Science, P.O. Box 5400, FI-02015 TKK, Finland (e-mail: [email protected], [email protected])
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Abstract

In this paper, a Gaifman–Shapiro-style module architecture is tailoredto the case of smodels programs under the stable model semantics. Thecomposition of smodels program modules is suitably limited by moduleconditions which ensure the compatibility of the module system with stablemodels. Hence the semantics of an entire smodels program dependsdirectly on stable models assigned to its modules. This result is formalized asa module theorem which truly strengthens V. Lifschitz and H.Turner's splitting-set theorem (June 1994, Splitting a logic program. InLogic Programming: Proceedings of the Eleventh InternationalConference on Logic Programming, Santa Margherita Ligure, Italy, P.V. Hentenryck, Ed. MIT Press, 23–37) for the class of smodelsprograms. To streamline generalizations in the future, the module theorem isfirst proved for normal programs and then extended to cover smodelsprograms using a translation from the latter class of programs to the formerclass. Moreover, the respective notion of module-level equivalence, namelymodular equivalence, is shown to be a proper congruencerelation: it is preserved under substitutions of modules that are modularlyequivalent. Principles for program decomposition are also addressed. Thestrongly connected components of the respective dependency graph can beexploited in order to extract a module structure when there is no explicita priori knowledge about the modules of a program. Thepaper includes a practical demonstration of tools that have been developed forautomated (de)composition of smodels programs.

Keywords

answer set programmingmodule systemcompositional semanticsstable model semanticsmodular equivalence
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 8 , Issue 5-6 , November 2008 , pp. 717 - 761
Copyright
Copyright © Cambridge University Press 2008

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