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Writing Declarative Specifications for Clauses

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Logics in Artificial Intelligence (JELIA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10021))

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Abstract

Modern satisfiability (SAT) solvers provide an efficient implementation of classical propositional logic. Their input language, however, is based on the conjunctive normal form (CNF) of propositional formulas. To use SAT solver technology in practice, a user must create the input clauses in one way or another. A typical approach is to write a procedural program that generates formulas on the basis of some input data relevant for the problem domain and translates them into CNF. In this paper, we propose a declarative approach where the intended clauses are specified in terms of rules in analogy to answer set programming (ASP). This allows the user to write first-order specifications for intended clauses in a schematic way by exploiting term variables. We develop a formal framework required to define the semantics of such specifications. Moreover, we provide an implementation harnessing state-of-the-art ASP grounders to accomplish the grounding step of clauses. As a result, we obtain a general-purpose clause-level grounding approach for SAT solvers. Finally, we illustrate the capabilities of our specification methodology in terms of combinatorial and application problems.

T. Schaub—Affiliated with Simon Fraser University, Canada, and IIIS Griffith University, Australia.

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Notes

  1. 1.

    Classical models can be encoded in ASP, e.g., using choice rules and integrity constraints [19].

  2. 2.

    http://research.ics.aalto.fi/software/asp/satgrnd/.

  3. 3.

    http://sat.inesc-id.pt/software/rpoly/.

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Acknowledgments

This work was funded by the Academy of Finland (251170), DFG (SCHA 550/9), as well as DAAD and the Academy of Finland (57071677 and 279121). We are grateful to João Marques-Silva and Inês Lynce for kindly providing us with the benchmark instances used in Sect. 4.

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Authors and Affiliations

  1. Helsinki Institute for Information Technology HIIT, Aalto University, Espoo, Finland

    Tomi Janhunen & Shahab Tasharrofi

  2. Institute for Informatics and Computational Science, University of Potsdam, Potsdam, Germany

    Martin Gebser, Roland Kaminski & Torsten Schaub

  3. INRIA Rennes, Bretagne Atlantique Research Centre, Rennes, France

    Torsten Schaub

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  1. Martin Gebser
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  2. Tomi Janhunen
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Correspondence to Tomi Janhunen .

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  1. Open University of Cyprus, Nicosia, Cyprus

    Loizos Michael

  2. University of Cyprus, Nicosia, Cyprus

    Antonis Kakas

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Gebser, M., Janhunen, T., Kaminski, R., Schaub, T., Tasharrofi, S. (2016). Writing Declarative Specifications for Clauses. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_17

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