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On finitely recursive programs1

Published online by Cambridge University Press:  11 March 2009

SABRINA BASELICE ,
PIERO A. BONATTI  and
GIOVANNI CRISCUOLO
SABRINA BASELICE
Affiliation:
Università di Napoli “Federico II”, Italy (e-mail: [email protected], [email protected], [email protected])
PIERO A. BONATTI
Affiliation:
Università di Napoli “Federico II”, Italy (e-mail: [email protected], [email protected], [email protected])
GIOVANNI CRISCUOLO
Affiliation:
Università di Napoli “Federico II”, Italy (e-mail: [email protected], [email protected], [email protected])
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Abstract

Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties; for example, ground queries are decidable, while in the general case the stable model semantics are Π11-hard. In this paper we prove that a larger class of programs, called finitely recursive programs, preserve most of the good properties of finitary programs under the stable model semantics, which are as follows: (i) finitely recursive programs enjoy a compactness property; (ii) inconsistency checking and skeptical reasoning are semidecidable; (iii) skeptical resolution is complete for normal finitely recursive programs. Moreover, we show how to check inconsistency and answer skeptical queries using finite subsets of the ground program instantiation. We achieve this by extending the splitting sequence theorem by Lifschitz and Turner: we prove that if the input program P is finitely recursive, then the partial stable models determined by any smooth splitting ω-sequence converge to a stable model of P.

Keywords

Answer set programming with infinite domainsinfinite stable modelsfinitary programscompactnessskeptical resolution
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 9 , Issue 2 , March 2009 , pp. 213 - 238
Copyright
Copyright © Cambridge University Press 2009

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