Abstract
We investigate the satisfiability problem, SAT(ID), of an extension of propositional logic with inductive definitions. We demonstrate how to extend existing SAT solvers to become SAT(ID) solvers, and provide an implementation on top of MiniSat. We also report on a performance study, in which our implementation exhibits the expected benefits: full use of the underlying SAT solver’s potential.
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References
Davis, M., Logemann, G., Loveland, D.W.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)
Denecker, M.: Extending Classical Logic with Inductive Definitions. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 703–717. Springer, Heidelberg (2000)
Denecker, M., De Schreye, D.: Justification semantics: A unifiying framework for the semantics of logic programs. In: LPNMR 1993, pp. 365–379. MIT Press, Cambridge (1993)
Denecker, M., Ternovska, E.: A Logic of Non-monotone Inductive Definitions and Its Modularity Properties. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 47–60. Springer, Heidelberg (2003)
Denecker, M., Vennekens, J.: Well-Founded Semantics and the Algebraic Theory of Non-monotone Inductive Definitions. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 84–96. Springer, Heidelberg (2007)
Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: clasp: A Conflict-Driven Answer Set Solver. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 260–265. Springer, Heidelberg (2007)
Gebser, M., Liu, L., Namasivayam, G., Neumann, A., Schaub, T., Truszczynski, M.: The First Answer Set Programming System Competition. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 3–17. Springer, Heidelberg (2007)
Van Gelder, A.: The alternating fixpoint of logic programs with negation. Journal of Computer and System Sciences 47(1), 185–221 (1993)
Van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)
Jackson, D.: Software Abstractions: Logic, Language, and Analysis. MIT Press, Cambridge (2006)
Lierler, Y.: cmodels – SAT-Based Disjunctive Answer Set Solver. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 447–451. Springer, Heidelberg (2005)
Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by sat solvers. Artif. Intell. 157(1-2), 115–137 (2004)
Lonc, Z., Truszczyński, M.: On the Problem of Computing the Well-Founded Semantics. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 673–687. Springer, Heidelberg (2000)
Marek, V.W., Truszczyński, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: a 25-Year Perspective, pp. 375–398. Springer, Heidelberg (1999)
Mariën, M., Wittocx, J., Denecker, M.: The IDP framework for declarative problem solving. In: Search and Logic: Answer Set Programming and SAT, pp. 19–34 (2006)
Mariën, M., Wittocx, J., Denecker, M.: Integrating Inductive Definitions in SAT. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 378–392. Springer, Heidelberg (2007)
Mariën, M., Wittocx, J., Denecker, M.: MidL: a SAT(ID) solver. In: 4th Workshop on Answer Set Programming: Advances in Theory and Implementation, pp. 303–308 (2007)
MiniSat(ID), http://www.cs.kuleuven.be/~dtai/krr/software/minisatid.html
Mitchell, D.G., Ternovska, E.: A framework for representing and solving NP search problems. In: AAAI 2005, pp. 430–435. AAAI Press / The MIT Press (2005)
Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: DAC 2001, pp. 530–535. ACM Press, New York (2001)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis–Putnam–Logemann–Loveland procedure to DPLL(t). J. ACM 53(6), 937–977 (2006)
Pelov, N., Ternovska, E.: Reducing Inductive Definitions to Propositional Satisfiability. In: Gabbrielli, M., Gupta, G. (eds.) ICLP 2005. LNCS, vol. 3668, pp. 221–234. Springer, Heidelberg (2005)
Silva, J.P.M., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Trans. Computers 48(5), 506–521 (1999)
Ward, J., Schlipf, J.S.: Answer Set Programming with Clause Learning. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 302–313. Springer, Heidelberg (2003)
Wittocx, J., Vennekens, J., Mariën, M., Denecker, M., Bruynooghe, M.: Predicate Introduction Under Stable and Well-Founded Semantics. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 242–256. Springer, Heidelberg (2006)
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Mariën, M., Wittocx, J., Denecker, M., Bruynooghe, M. (2008). SAT(ID): Satisfiability of Propositional Logic Extended with Inductive Definitions. In: Kleine Büning, H., Zhao, X. (eds) Theory and Applications of Satisfiability Testing – SAT 2008. SAT 2008. Lecture Notes in Computer Science, vol 4996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79719-7_20
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DOI: https://doi.org/10.1007/978-3-540-79719-7_20
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