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A decidable subclass of finitary programs


Answer set programming—the most popular problem solving paradigm based on logic programs—has been recently extended to support uninterpreted function symbols (Syrjänen 2001, Bonatti 2004; Simkus and Eiter 2007; Gebser et al. 2007; Baselice et al. 2009; Calimeri et al. 2008). All of these approaches have some limitation. In this paper we propose a class of programs called FP2 that enjoys a different trade-off between expressiveness and complexity. FP2 is inspired by the extension of finitary normal programs with local variables introduced in (Bonatti 2004, Section 5). FP2 programs enjoy the following unique combination of properties: (i) the ability of expressing predicates with infinite extensions; (ii) full support for predicates with arbitrary arity; (iii) decidability of FP2 membership checking; (iv) decidability of skeptical and credulous stable model reasoning for call-safe queries. Odd cycles are supported by composing FP2 programs with argument restricted programs.

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P. A. Bonatti 2004. Reasoning with infinite stable models. Artificial Intelligence 156, 1, 75111.

P. A. Bonatti 2008. Erratum to: Reasoning with infinite stable models [Artificial Intelligence 156 (1) (2004) 75–111]. Artificial Intelligence 172, 15, 18331835.

A. Bossi , N. Cocco , and M. Fabris 1994. Norms on terms and their use in proving universal termination of a logic program. Theoretical Computer Science 124, 2, 297328.

M. Gelfond and V. Lifschitz 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 3–4, 365386.

J. W. Lloyd 1984. Foundations of Logic Programming, 1st ed.Springer.

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Theory and Practice of Logic Programming
  • ISSN: 1471-0684
  • EISSN: 1475-3081
  • URL: /core/journals/theory-and-practice-of-logic-programming
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