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Achieving compositionality of the stable model semantics for smodels 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: Emilia.Oikarinen@tkk.fi, Tomi.Janhunen@tkk.fi)
TOMI JANHUNEN
Affiliation:
Helsinki University of Technology, TKK, Department of Information and Computer Science, P.O. Box 5400, FI-02015 TKK, Finland (e-mail: Emilia.Oikarinen@tkk.fi, Tomi.Janhunen@tkk.fi)
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Abstract

In this paper, a Gaifman–Shapiro-style module architecture is tailored to the case of smodels programs under the stable model semantics. The composition of smodels program modules is suitably limited by module conditions which ensure the compatibility of the module system with stable models. Hence the semantics of an entire smodels program depends directly on stable models assigned to its modules. This result is formalized as a module theorem which truly strengthens V. Lifschitz and H. Turner's splitting-set theorem (June 1994, Splitting a logic program. In Logic Programming: Proceedings of the Eleventh International Conference on Logic Programming, Santa Margherita Ligure, Italy, P. V. Hentenryck, Ed. MIT Press, 23–37) for the class of smodels programs. To streamline generalizations in the future, the module theorem is first proved for normal programs and then extended to cover smodels programs using a translation from the latter class of programs to the former class. Moreover, the respective notion of module-level equivalence, namely modular equivalence, is shown to be a proper congruence relation: it is preserved under substitutions of modules that are modularly equivalent. Principles for program decomposition are also addressed. The strongly connected components of the respective dependency graph can be exploited in order to extract a module structure when there is no explicit a priori knowledge about the modules of a program. The paper includes a practical demonstration of tools that have been developed for automated (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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