On finitely recursive programs

Abstract

Disjunctivefinitary programsare 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, calledfinitely 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 programPis finitely recursive, then the partial stable models determined by any smooth splitting ω-sequence converge to a stable model ofP.