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answer set programming with infinite domains

Theory and Practice of Logic Programming (1)

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On finitely recursive programs 1
SABRINA BASELICE, PIERO A. BONATTI, GIOVANNI CRISCUOLO
Journal:

Theory and Practice of Logic Programming / Volume 9 / Issue 2 / March 2009

Published online by Cambridge University Press:

11 March 2009, pp. 213-238
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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.