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Optimizing Answer Set Computation via Heuristic-Based Decomposition

  • FRANCESCO CALIMERI (a1), SIMONA PERRI (a1) and JESSICA ZANGARI (a1)
Abstract

Answer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and non-monotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are computed by an ASP system. Different, semantically equivalent, programs can be defined for the same problem; however, performance of systems evaluating them might significantly vary. We propose an approach for automatically transforming an input logic program into an equivalent one that can be evaluated more efficiently. One can make use of existing tree-decomposition techniques for rewriting selected rules into a set of multiple ones; the idea is to guide and adaptively apply them on the basis of proper new heuristics, to obtain a smart rewriting algorithm to be integrated into an ASP system. The method is rather general: it can be adapted to any system and implement different preference policies. Furthermore, we define a set of new heuristics tailored at optimizing grounding, one of the main phases of the ASP computation; we use them in order to implement the approach into the ASP system DLV, in particular into its grounding subsystem ℐ-DLV, and carry out an extensive experimental activity for assessing the impact of the proposal.

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This work has been partially supported by the Italian region Calabria under project “DLV Large Scale” (CUP J28C17000220006) POR Calabria FESR 2014–2020 and by both the European Union and the Italian Ministry of Economic Development under the project EU H2020 PON I&C 2014–2020 “Smarter Solutions in the Big Data World – S2BDW” (CUP B28I17000250008). This work is the extended version of a paper originally appeared in the Proceedings of 20th Symposium on Practical Aspects of Declarative Languages (PADL 2018), January 8–9, 2018, Los Angeles, USA. Program chairs were Kevin Hamlen and Nicola Leone. The paper presents new material that integrates and extends what has been reported in the original paper; in particular, it provides the reader with proper preliminaries (omitted in the original paper for space constraints), more detailed discussions on the proposed techniques and richer comparisons with related approaches, along with an extended number of examples. Furthermore, a more thorough experimental activity is presented, discussed in part in the main text and in part in Appendices in the Supplementary Material, that covers also new domains that were unexplored in the original paper.

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Abseher, M., Musliu, N. and Woltran, S. 2017. htd – A free, open-source framework for (customized) tree decompositions and beyond. In Proceedings of Integration of AI and OR Techniques in Constraint Programming – 14th International Conference, CPAIOR 2017, Padua, Italy, June 5–8, 2017, Salvagnin, D. and Lombardi, M., Eds. Lecture Notes in Computer Science, vol. 10335. Springer, 376386.
Alviano, M., Calimeri, F., Dodaro, C., Fuscà, D., Leone, N., Perri, S., Ricca, F., Veltri, P. and Zangari, J. 2017. The ASP system DLV2. In Proceedings of Logic Programming and Nonmonotonic Reasoning – 14th International Conference, LPNMR 2017, Espoo, Finland, July 3–6, 2017, Balduccini, M. and Janhunen, T., Eds. Lecture Notes in Computer Science, vol. 10377. Springer, 215221.
Alviano, M., Dodaro, C., Leone, N. and Ricca, F. 2015. Advances in WASP. In Proceedings of Logic Programming and Nonmonotonic Reasoning – 13th International Conference, LPNMR 2015, Lexington, KY, USA, September 27–30, 2015, Calimeri, F., Ianni, G. and Truszczynski, M., Eds. Lecture Notes in Computer Science, vol. 9345. Springer, 4054.
Alviano, M., Faber, W., Greco, G. and Leone, N. 2012. Magic sets for disjunctive datalog programs. Artificial Intelligence 187, 156192.
Ben-Eliyahu, R. and Dechter, R. 1994. Propositional semantics for disjunctive logic programs. Annals of Mathematics and Artificial Intelligence 12, 1–2, 5387.
Ben-Eliyahu-Zohary, R. and Palopoli, L. 1997. Reasoning with minimal models: Efficient algorithms and applications. Artificial Intelligence 96, 2, 421449.
Bichler, M., Morak, M. and Woltran, S. 2016a. lpopt: A rule optimization tool for answer set programming. In Logic-Based Program Synthesis and Transformation – 26th International Symposium, LOPSTR 2016, Edinburgh, UK, September 6–8, 2016, Revised Selected Papers, Hermenegildo, M. V. and López-Garca, P., Eds. Lecture Notes in Computer Science, vol. 10184. Springer, 114130.
Bichler, M., Morak, M. and Woltran, S. 2016b. The power of non-ground rules in answer set programming. Theory and Practice of Logic Programming 16, 5–6, 552569.
Bliem, B., Moldovan, M., Morak, M. and Woltran, S. 2017. The impact of treewidth on ASP grounding and solving. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19–25, 2017, Sierra, C., Ed. ijcai.org, 852858.
Brewka, G., Eiter, T. and Truszczynski, M. 2011. Answer set programming at a glance. Communications of the ACM 54, 12, 92103.
Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F. and Schaub, T. 2013. ASP-Core-2: 4th ASP competition official input language format. https://www.mat.unical.it/aspcomp2013/files/ASP-CORE-2.01c.pdf.
Calimeri, F., Fuscà, D., Perri, S. and Zangari, J. 2017a. The ASP instantiator I-DLV. In PAoASP. Espoo, Finland.
Calimeri, F., Fuscà, D., Perri, S. and Zangari, J. 2017b. I-DLV: the new intelligent grounder of DLV. Intelligenza Artificiale 11, 1, 520.
Calimeri, F., Gebser, M., Maratea, M. and Ricca, F. 2016. Design and results of the fifth answer set programming competition. Artificial Intelligence 231, 151181.
Calimeri, F., Perri, S. and Ricca, F. 2008. Experimenting with parallelism for the instantiation of ASP programs. Journal of Algorithms 63, 1–3, 3454.
Dantsin, E., Eiter, T., Gottlob, G. and Voronkov, A. 2001. Complexity and expressive power of logic programming. ACM Computing Surveys 33, 3, 374425.
Dao-Tran, M., Eiter, T., Fink, M., Weidinger, G. and Weinzierl, A. 2012. Omiga : An open minded grounding on-the-fly answer set solver. In Proceedings of Logics in Artificial Intelligence – 13th European Conference, JELIA 2012, Toulouse, France, September 26–28, 2012., del Cerro, L. F., Herzig, A. and Mengin, J., Eds. Lecture Notes in Computer Science, vol. 7519. Springer, 480483.
Eiter, T., Gottlob, G. and Mannila, H. 1997. Disjunctive datalog. ACM Transactions on Database Systems 22, 3, 364418.
Eiter, T., Kaminski, T. and Weinzierl, A. 2017. Lazy-grounding for answer set programs with external source access. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19–25, 2017, Sierra, C., Ed. ijcai.org, 10151022.
Faber, W., Leone, N. and Perri, S. 2012. The intelligent grounder of DLV. In Correct Reasoning – Essays on Logic-Based AI in Honour of Vladimir Lifschitz. Lecture Notes in Computer Science, vol. 7265, Springer 247264.
Fuscà, D., Calimeri, F., Zangari, J. and Perri, S. 2017. I-DLV+MS: preliminary report on an automatic ASP solver selector. In Proceedings of the 24th RCRA International Workshop on Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion 2017 co-located with the 16th International Conference of the Italian Association for Artificial Intelligence (AI*IA 2017), Bari, Italy, November 14–15, 2017., Maratea, M. and Serina, I., Eds. CEUR Workshop Proceedings, vol. 2011. CEUR-WS.org, 2632.
Gebser, M., Kaminski, R., Kaufmann, B., Romero, J. and Schaub, T. 2015. Progress in clasp series 3. In Proceedings of Logic Programming and Nonmonotonic Reasoning – 13th International Conference, LPNMR 2015, Lexington, KY, USA, September 27–30, 2015, Calimeri, F., Ianni, G. and Truszczynski, M., Eds. Lecture Notes in Computer Science, vol. 9345. Springer, 368383.
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2014. Clingo = ASP + control: Preliminary report. CoRR abs/1405.3694.
Gebser, M., Kaminski, R., König, A. and Schaub, T. 2011. Advances in gringo series 3. In Proceedings of Logic Programming and Nonmonotonic Reasoning – 11th International Conference, LPNMR 2011, Vancouver, Canada, May 16–19, 2011, Delgrande, J. P. and Faber, W., Eds. Lecture Notes in Computer Science, vol. 6645. Springer, 345351.
Gebser, M., Kaufmann, B. and Schaub, T. 2012. Conflict-driven answer set solving: From theory to practice. Artificial Intelligence 187, 5289.
Gebser, M., Maratea, M. and Ricca, F. 2015. The design of the sixth answer set programming competition – report. In Proceedings of Logic Programming and Nonmonotonic Reasoning – 13th International Conference, LPNMR 2015, Lexington, KY, USA, September 27–30, 2015, Calimeri, F., Ianni, G. and Truszczynski, M., Eds. Lecture Notes in Computer Science, vol. 9345. Springer, 531544.
Gebser, M., Maratea, M. and Ricca, F. 2016. What’s hot in the answer set programming competition. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, February 12–17, 2016, Phoenix, Arizona, USA, Schuurmans, D. and Wellman, M. P., Eds. AAAI Press, 43274329.
Gebser, M., Maratea, M. and Ricca, F. 2017. The design of the seventh answer set programming competition. In Logic Programming and Nonmonotonic Reasoning – 14th International Conference, LPNMR 2017, Espoo, Finland, July 3–6, 2017, Balduccini, M. and Janhunen, T., Eds. Lecture Notes in Computer Science, vol. 10377. Springer, 39.
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 3/4, 365386.
Giunchiglia, E., Lierler, Y. and Maratea, M. 2006. Answer set programming based on propositional satisfiability. Journal of Automated Reasoning 36, 4, 345377.
Gottlob, G., Greco, G., Leone, N. and Scarcello, F. 2016. Hypertree decompositions: Questions and answers. In Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2016, San Francisco, CA, USA, June 26–July 01, 2016, Milo, T. and Tan, W., Eds. ACM, 5774.
Gottlob, G., Grohe, M., Musliu, N., Samer, M. and Scarcello, F. 2005. Hypertree decompositions: Structure, algorithms, and applications. In Graph-Theoretic Concepts in Computer Science, 31st International Workshop, WG 2005, Metz, France, June 23–25, 2005, Revised Selected Papers, Kratsch, D., Ed. Lecture Notes in Computer Science, vol. 3787. Springer, 115.
Gottlob, G., Leone, N. and Scarcello, F. 2001. Hypertree decompositions: A survey. In Proceedings of Mathematical Foundations of Computer Science 2001, 26th International Symposium, MFCS 2001 Marianske Lazne, Czech Republic, August 27–31, 2001, Sgall, J., Pultr, A. and Kolman, P., Eds. Lecture Notes in Computer Science, vol. 2136. Springer, 3757.
Janhunen, T., Niemelä, I., Seipel, D., Simons, P. and You, J. 2006. Unfolding partiality and disjunctions in stable model semantics. ACM Transactions on Computational Logic 7, 1, 137.
Kaufmann, B., Leone, N., Perri, S. and Schaub, T. 2016. Grounding and solving in answer set programming. AI Magazine 37, 3, 2532.
Lefèvre, C., Béatrix, C., Stéphan, I. and Garcia, L. 2017. Asperix, a first-order forward chaining approach for answer set computing. Theory and Practice of Logic Programming 17, 3, 266310.
Leone, N., Perri, S. and Scarcello, F. 2001. Improving ASP instantiators by join-ordering methods. In Proceedings of Logic Programming and Nonmonotonic Reasoning, 6th International Conference, LPNMR 2001, Vienna, Austria, September 17–19, 2001, Eiter, T., Faber, W. and Truszczynski, M., Eds. Lecture Notes in Computer Science, vol. 2173. Springer, 280294.
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S. and Scarcello, F. 2006. The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7, 3, 499562.
Lifschitz, V. 1999. Answer set planning. In Logic Programming: The 1999 International Conference, Las Cruces, New Mexico, USA, November 29 – December 4, 1999, Schreye, D. D., Ed. MIT Press, 2337.
Morak, M. and Woltran, S. 2012. Preprocessing of complex non-ground rules in answer set programming. In Technical Communications of the 28th International Conference on Logic Programming, ICLP 2012, September 4–8, 2012, Budapest, Hungary, Dovier, A. and Costa, V. S., Eds. LIPIcs, vol. 17. Schloss Dagstuhl – Leibniz–Zentrum fuer Informatik, 247258.
Palù, A. D., Dovier, A., Pontelli, E. and Rossi, G. 2009. GASP: answer set programming with lazy grounding. Fundamenta Informaticae 96, 3, 297322.
Perri, S., Ricca, F. and Sirianni, M. 2013. Parallel instantiation of ASP programs: techniques and experiments. TPLP 13, 2, 253278.
Perri, S., Scarcello, F., Catalano, G. and Leone, N. 2007. Enhancing DLV instantiator by backjumping techniques. Annals of Mathematics and Artificial Intelligence 51, 2–4, 195228.
Robertson, N. and Seymour, P. D. 1986. Graph minors. II. algorithmic aspects of tree-width. J. Algorithms 7, 3, 309322.
Simona, P., and Zangari, J. 2018. Optimizing answer set computation via heuristic-based decomposition. In Practical Aspects of Declarative Languages - 20th International Symposium, PADL 2018, Los Angeles, CA, USA, January 8-9, 2018, Proceedings, Calimeri, F., Hamlen, K. W. and Leone, N., Eds. Lecture Notes in Computer Science, vol. 10702. Springer, 135151.
Simons, P., Niemelä, I. and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138, 1–2, 181234.
Syrjänen, T. 2001. Omega-restricted logic programs. In Proceedings of Logic Programming and Nonmonotonic Reasoning, 6th International Conference, LPNMR 2001, Vienna, Austria, September 17–19, 2001, Eiter, T., Faber, W. and Truszczynski, M., Eds. Lecture Notes in Computer Science, vol. 2173. Springer, 267279.
Ullman, J. D. 1988. Principles of Database and Knowledge-Base Systems, Volume I. Principles of computer science series, vol. 14. Computer Science Press.
Ward, J. and Schlipf, J. S. 2004. Answer set programming with clause learning. In Proceedings of Logic Programming and Nonmonotonic Reasoning, 7th International Conference, LPNMR 2004, Fort Lauderdale, FL, USA, January 6–8, 2004, Lifschitz, V. and Niemelä, I., Eds. Lecture Notes in Computer Science, vol. 2923. Springer, 302313.
Weinzierl, A. 2017. Blending lazy-grounding and CDNL search for answer-set solving. In Proceedings of Logic Programming and Nonmonotonic Reasoning – 14th International Conference, LPNMR 2017, Espoo, Finland, July 3–6, 2017, Balduccini, M. and Janhunen, T., Eds. Lecture Notes in Computer Science, vol. 10377. Springer, 191204.
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