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Cautious reasoning in ASP via minimal models and unsatisfiable cores

Published online by Cambridge University Press:  10 August 2018

MARIO ALVIANO ,
CARMINE DODARO Open the ORCID record for CARMINE DODARO [Opens in a new window] ,
MATTI JÄRVISALO ,
MARCO MARATEA  and
ALESSANDRO PREVITI
MARIO ALVIANO
Affiliation:
DEMACS, University of Calabria, Italy (e-mail: [email protected])
CARMINE DODARO
Affiliation:
DIBRIS, University of Genova, Italy (e-mail: [email protected])
MATTI JÄRVISALO
Affiliation:
HIIT, Department of Computer Science, University of Helsinki, Finland (e-mail: [email protected])
MARCO MARATEA
Affiliation:
DIBRIS, University of Genova, Italy (e-mail: [email protected])
ALESSANDRO PREVITI
Affiliation:
HIIT, Department of Computer Science, University of Helsinki, Finland (e-mail: [email protected])
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Abstract

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Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting—among other reasoning modes—the central task of query answering. In the propositional case, query answering amounts to computing cautious consequences of the input program among the atoms in a given set of candidates, where a cautious consequence is an atom belonging to all stable models. Currently, the most efficient algorithms either iteratively verify the existence of a stable model of the input program extended with the complement of one candidate, where the candidate is heuristically selected, or introduce a clause enforcing the falsity of at least one candidate, so that the solver is free to choose which candidate to falsify at any time during the computation of a stable model. This paper introduces new algorithms for the computation of cautious consequences, with the aim of driving the solver to search for stable models discarding more candidates. Specifically, one of such algorithms enforces minimality on the set of true candidates, where different notions of minimality can be used, and another takes advantage of unsatisfiable cores computation. The algorithms are implemented in wasp, and experiments on benchmarks from the latest ASP competitions show that the new algorithms perform better than the state of the art.

Keywords

Answer Set ProgrammingCautious ReasoningQuery Answering
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 18 , Special Issue 3-4: 34th International Conference on Logic Programming , July 2018 , pp. 319 - 336
Copyright
Copyright © Cambridge University Press 2018 

References

Alviano, M. 2017a. Model enumeration in propositional circumscription via unsatisfiable core analysis. Theory and Practice of Logic Programming 17, 5–6, 708–725.Google Scholar
Alviano, M. 2017b. The pyglaf argumentation reasoner. In Technical Communications of the International Conference on Logic Programming. OASICS, vol. 58. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2:1–2:3.Google Scholar
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 International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 10377. Springer, 215–221.Google Scholar
Alviano, M. and Dodaro, C. 2016. Anytime answer set optimization via unsatisfiable core shrinking. Theory and Practice of Logic Programming 16, 5–6, 533–551.Google Scholar
Alviano, M. and Dodaro, C. 2017. Unsatisfiable core shrinking for anytime answer set optimization. In International Joint Conference on Artificial Intelligence. ijcai.org, 4781–4785.Google Scholar
Alviano, M., Dodaro, C., Faber, W., Leone, N., and Ricca, F. 2013. WASP: A native ASP solver based on constraint learning. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 8148. Springer, 54–66.Google Scholar
Alviano, M., Dodaro, C., Leone, N., and Ricca, F. 2015. Advances in WASP. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 9345. Springer, 40–54.Google Scholar
Alviano, M., Dodaro, C., Marques-Silva, J., and Ricca, F. 2015. Optimum stable model search: algorithms and implementation. Journal of Logic and Computation. To appear.Google Scholar
Alviano, M., Dodaro, C., and Ricca, F. 2014. Anytime computation of cautious consequences in answer set programming. Theory and Practice of Logic Programming 14, 4–5, 755–770.Google Scholar
Alviano, M., Dodaro, C., and Ricca, F. 2015. A MaxSAT algorithm using cardinality constraints of bounded size. In International Joint Conference on Artificial Intelligence. AAAI Press, 2677–2683.Google Scholar
Alviano, M. and Faber, W. 2011. Dynamic magic sets and super-coherent answer set programs. AI Communications 24, 2, 125–145.Google Scholar
Alviano, M., Faber, W., Greco, G., and Leone, N. 2012. Magic sets for disjunctive datalog programs. Artificial Intelligence 187, 156–192.Google Scholar
Alviano, M., Faber, W., and Leone, N. 2010. Disjunctive ASP with functions: Decidable queries and effective computation. Theory and Practice of Logic Programming 10, 4–6, 497–512.Google Scholar
Alviano, M., Faber, W., Leone, N., Perri, S., Pfeifer, G., and Terracina, G. 2010. The Disjunctive Datalog System DLV. In Datalog Reloaded. Lecture Notes in Computer Science, vol. 6702. Springer, 282–301.Google Scholar
Amendola, G., Dodaro, C., Faber, W., Leone, N., and Ricca, F. 2017. On the computation of paracoherent answer sets. In AAAI Conference on Artificial Intelligence. AAAI Press, 1034–1040.Google Scholar
Arenas, M., Bertossi, L. E., and Chomicki, J. 2003. Answer sets for consistent query answering in inconsistent databases. Theory and Practice of Logic Programming 3, 4–5, 393–424.Google Scholar
Baral, C. 2010. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.Google Scholar
Brewka, G. and Eiter, T. 2007. Equilibria in heterogeneous nonmonotonic multi-context systems. In AAAI Conference on Artificial Intelligence. AAAI Press, 385–390.Google Scholar
Brewka, G., Eiter, T., and Truszczynski, M. 2011. Answer set programming at a glance. Communications of the ACM 54, 12, 92–103.Google Scholar
Brewka, G., Roelofsen, F., and Serafini, L. 2007. Contextual default reasoning. In International Joint Conference on Artificial Intelligence. 268–273.Google Scholar
Brochenin, R. and Maratea, M. 2015. Abstract answer set solvers for cautious reasoning. In Technical Communications of the International Conference on Logic Programming. CEUR Workshop Proceedings, vol. 1433. CEUR-WS.org.Google Scholar
Bry, F. and Yahya, A. H. 2000. Positive unit hyperresolution tableaux and their application to minimal model generation. Journal of Automated Reasoning 25, 1, 35–82.Google Scholar
Calimeri, F., Gebser, M., Maratea, M., and Ricca, F. 2016. Design and results of the Fifth Answer Set Programming Competition. Artificial Intelligence 231, 151–181.Google Scholar
Calimeri, F., Ianni, G., and Ricca, F. 2014. The third open answer set programming competition. Theory and Practice of Logic Programming 14, 1, 117–135.Google Scholar
DI ROSA, E., Giunchiglia, E., and Maratea, M. 2010. Solving satisfiability problems with preferences. Constraints 15, 4, 485–515.Google Scholar
Dodaro, C., Alviano, M., Faber, W., Leone, N., Ricca, F., and Sirianni, M. 2011. The birth of a WASP: preliminary report on a new ASP solver. In Italian Conference on Computational Logic, Fioravanti, F., Ed. CEUR Workshop Proceedings, vol. 810. CEUR-WS.org, 99–113.Google Scholar
Dodaro, C., Gasteiger, P., Leone, N., Musitsch, B., Ricca, F., and Schekotihin, K. 2016. Combining answer set programming and domain heuristics for solving hard industrial problems (application paper). Theory and Practice of Logic Programming 16, 5–6, 653–669.Google Scholar
Eiter, T. 2005. Data integration and answer set programming. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 3662. Springer, 13–25.Google Scholar
Eiter, T., Gottlob, G., and Mannila, H. 1997. Disjunctive datalog. ACM Transactions on Database Systems 22, 3, 364–418.Google Scholar
Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R., and Tompits, H. 2008. Combining answer set programming with description logics for the semantic web. Artificial Intelligence 172, 12–13, 1495–1539.Google Scholar
Gebser, M., Kaminski, R., König, A., and Schaub, T. 2011. Advances in gringo series 3. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 6645. Springer, 345–351.Google Scholar
Gebser, M., Kaufmann, B., Romero, J., Otero, R., Schaub, T., and Wanko, P. 2013. Domain-specific heuristics in answer set programming. In AAAI Conference on Artificial Intelligence, desJardins, M. and Littman, M. L., Eds. AAAI Press.Google Scholar
Gebser, M., Kaufmann, B., and Schaub, T. 2012. Conflict-driven answer set solving: From theory to practice. Artificial Intelligence 187, 52–89.Google Scholar
Gebser, M., Maratea, M., and Ricca, F. 2017. The Sixth Answer Set Programming Competition. Journal of Artificial Intelligence Research 60, 41–95.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In International Conference and Symposium on Logic Programming. MIT Press, 1070–1080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 3/4, 365–386.Google Scholar
Giunchiglia, E., Leone, N., and Maratea, M. 2008. On the relation among answer set solvers. Annals of Mathematics and Artificial Intelligence 53, 1–4, 169–204.Google Scholar
Hasegawa, R., Fujita, H., and Koshimura, M. 2000. Efficient minimal model generation using branching lemmas. In International Conference on Automated Deduction. Lecture Notes in Computer Science, vol. 1831. Springer, 184–199.Google Scholar
Janhunen, T. and Niemelä, I. 2016. The answer set programming paradigm. AI Magazine 37, 3, 13–24.Google Scholar
Janota, M., Lynce, I. and Marques-Silva, J. 2015. Algorithms for computing backbones of propositional formulae. AI Communications 28, 2, 161–177.Google Scholar
Janota, M. and Marques-Silva, J. 2016. On the query complexity of selecting minimal sets for monotone predicates. Artificial Intelligence 233, 73–83.Google Scholar
Kaufmann, B., Leone, N., Perri, S., and Schaub, T. 2016. Grounding and solving in answer set programming. AI Magazine 37, 3, 25–32.Google Scholar
Koshimura, M., Nabeshima, H., Fujita, H., and Hasegawa, R. 2009. Minimal model generation with respect to an atom set. In International Workshop on First-Order Theorem Proving. CEUR Workshop Proceedings, vol. 556. CEUR-WS.org.Google Scholar
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, 499–562.Google Scholar
Lifschitz, V. 2016. Answer sets and the language of answer set programming. AI Magazine 37, 3, 7–12.Google Scholar
Manna, M., Ricca, F., and Terracina, G. 2013. Consistent query answering via ASP from different perspectives: Theory and practice. Theory and Practice of Logic Programming 13, 2, 227–252.Google Scholar
Manna, M., Ricca, F., and Terracina, G. 2015. Taming primary key violations to query large inconsistent data via ASP. Theory and Practice of Logic Programming 15, 4–5, 696–710.Google Scholar
Marek, V. and Truszczyński, M. 1999. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: A 25-Year Perspective. Springer, 375–398.Google Scholar
Niemelä, I. 1996. A tableau calculus for minimal model reasoning. In International Workshop on Theorem Proving with Analytic Tableaux and Related Methods. Lecture Notes in Computer Science, vol. 1071. Springer, 278–294.Google Scholar
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 3–4, 241–273.Google Scholar
Previti, A. and Järvisalo, M. 2018. A preference-based approach to backbone computation with application to argumentation. In ACM/SIGAPP Symposium on Applied Computing. ACM. To appear.Google Scholar
Silva, J. P. M. and Sakallah, K. A. 1999. GRASP: A search algorithm for propositional satisfiability. IEEE Transactions on Computers 48, 5, 506–521.Google Scholar
Zhu, C. S., Weissenbacher, G., Sethi, D., and Malik, S. 2011. SAT-based techniques for determining backbones for post-silicon fault localisation. In IEEE International High Level Design Validation and Test Workshop. IEEE Computer Society, 84–91.Google Scholar