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Shared aggregate sets in answer set programming

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]  and
MARCO MARATEA
MARIO ALVIANO
Affiliation:
DEMACS, University of Calabria, Italy (e-mail: [email protected])
CARMINE DODARO
Affiliation:
DIBRIS, University of Genova, Italy (e-mails: [email protected], [email protected])
MARCO MARATEA
Affiliation:
DIBRIS, University of Genova, Italy (e-mails: [email protected], [email protected])
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Abstract

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Aggregates are among the most frequently used linguistic extensions of answer set programming. The result of an aggregation may introduce new constants during the instantiation of the input program, a feature known as value invention. When the aggregation involves literals whose truth value is undefined at instantiation time, modern grounders introduce several instances of the aggregate, one for each possible interpretation of the undefined literals. This paper introduces new data structures and techniques to handle such cases, and more in general aggregations on the same aggregate set identified in the ground program in input. The proposed solution reduces the memory footprint of the solver without sacrificing efficiency. On the contrary, the performance of the solver may improve thanks to the addition of some simple entailed clauses which are not easily discovered otherwise, and since redundant computation is avoided during propagation. Empirical evidence of the potential impact of the proposed solution is given.

Keywords

answer set programmingaggregations in logic programmingefficient computation
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. 301 - 318
Copyright
Copyright © Cambridge University Press 2018 

References

Aavani, A., Mitchell, D. G., and Ternovska, E. 2013. New encoding for translating pseudo-boolean constraints into SAT. In Symposium on Abstraction, Reformulation, and Approximation. AAAI.Google Scholar
Abío, I., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E., and Mayer-Eichberger, V. 2012. A New Look at BDDs for Pseudo-Boolean Constraints. Journal of Artificial Intelligence Research 45, 443–480.Google Scholar
Abío, I. and Stuckey, P. J. 2012. Conflict directed lazy decomposition. In International Conference on Principles and Practice of Constraint Programming. Lecture Notes in Computer Science, vol. 7514. Springer, 70–85.Google Scholar
Alviano, M. 2011. Efficient recursive aggregate evaluation in logic programming. Intelligenza Artificiale 5, 2, 207–215.Google Scholar
Alviano, M. 2016. Evaluating answer set programming with non-convex recursive aggregates. Fundamenta Informaticae 149, 1–2, 1–34.Google Scholar
Alviano, M., Calimeri, F., Charwat, G., and et al. 2013. The Fourth Answer Set Programming Competition: Preliminary Report. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 8148. Springer, 42–53.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., Calimeri, F., Faber, W., Leone, N., and Perri, S. 2011. Unfounded sets and well-founded semantics of answer set programs with aggregates. Journal of Artificial Intelligence Research 42, 487–527.Google Scholar
Alviano, M. and Dodaro, C. 2016a. 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. 2016b. Completion of disjunctive logic programs. In International Joint Conference on Artificial Intelligence. IJCAI/AAAI Press, 886–892.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., 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. and Faber, W. 2013. The complexity boundary of answer set programming with generalized atoms under the FLP semantics. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 8148. Springer, 67–72.Google Scholar
Alviano, M., Faber, W., and Gebser, M. 2015. Rewriting recursive aggregates in answer set programming: back to monotonicity. Theory and Practice of Logic Programming 15, 4–5, 559–573.Google Scholar
Alviano, M., Faber, W., and Gebser, M. 2016. From non-convex aggregates to monotone aggregates in ASP. In International Joint Conference on Artificial Intelligence. IJCAI/AAAI Press, 4100–4194.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., 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
Alviano, M., Faber, W., and Strass, H. 2016. Boolean functions with ordered domains in answer set programming. In AAAI Conference on Artificial Intelligence. AAAI Press, 879–885.Google Scholar
Alviano, M., Faber, W., and Woltran, S. 2014. Complexity of super-coherence problems in ASP. Theory and Practice of Logic Programming 14, 3, 339–361.Google Scholar
Alviano, M., Greco, G., and Leone, N. 2011. Dynamic magic sets for programs with monotone recursive aggregates. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 6645. Springer, 148–160.Google Scholar
Alviano, M. and Leone, N. 2015. Complexity and compilation of gz-aggregates in answer set programming. Theory and Practice of Logic Programming 15, 4–5, 574–587.Google Scholar
Alviano, M. and Leone, N. 2016. On the properties of gz-aggregates in answer set programming. In International Joint Conference on Artificial Intelligence. IJCAI/AAAI Press, 4105–4109.Google Scholar
Andres, B., Kaufmann, B., Matheis, O., and Schaub, T. 2012. Unsatisfiability-based optimization in clasp. In Technical Communications of the International Conference on Logic Programming. LIPIcs, vol. 17. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 211–221.Google Scholar
Bailleux, O., Boufkhad, Y., and Roussel, O. 2009. New encodings of pseudo-boolean constraints into CNF. In The International Conferences on Theory and Applications of Satisfiability Testing. Lecture Notes in Computer Science, vol. 5584. Springer, 181–194.Google Scholar
Banbara, M., Kaufmann, B., Ostrowski, M., and Schaub, T. 2017. Clingcon: The next generation. Theory and Practice of Logic Programming 17, 4, 408–461.Google Scholar
Bartholomew, M., Lee, J., and Meng, Y. 2011. First-order semantics of aggregates in answer set programming via modified circumscription. In Logical Formalizations of Commonsense Reasoning AAAI Spring Symposium. AAAI.Google Scholar
Baselice, S., Bonatti, P. A., and Gelfond, M. 2005. Towards an integration of answer set and constraint solving. In International Conference on Logic Programming. Lecture Notes in Computer Science, vol. 3668. Springer, 52–66.Google Scholar
Bomanson, J., Gebser, M., and Janhunen, T. 2014. Improving the normalization of weight rules in answer set programs. In European Conference on Logics in Artificial Intelligence. Lecture Notes in Computer Science, vol. 8761. Springer, 166–180.Google Scholar
Bomanson, J., Gebser, M., Janhunen, T., Kaufmann, B., and Schaub, T. 2015. Answer set programming modulo acyclicity. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 9345. Springer, 143–150.Google Scholar
Bomanson, J. and Janhunen, T. 2013. Normalizing cardinality rules using merging and sorting constructions. In Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 8148. Springer, 187–199.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
Bruynooghe, M., Blockeel, H., Bogaerts, B., de Cat, B., Pooter, S. D., Jansen, J., Labarre, A., Ramon, J., Denecker, M., and Verwer, S. 2015. Predicate logic as a modeling language: modeling and solving some machine learning and data mining problems with IDP3. Theory and Practice of Logic Programming 15, 6, 783–817.Google Scholar
Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F., and Schaub, T. 2013. ASP-Core-2 Input Language Format.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
Cuteri, B., Dodaro, C., Ricca, F. and Schüller, P. 2017. Constraints, lazy constraints, or propagators in ASP solving: An empirical analysis. Theory and Practice of Logic Programming 17, 5–6, 780–799.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. 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
Eén, N. and Sörensson, N. 2006. Translating pseudo-boolean constraints into SAT. Journal on Satisfiability, Boolean Modeling and Computation 2, 1–4, 1–26.Google Scholar
Faber, W., Leone, N., Maratea, M., and Ricca, F. 2011. Look-back techniques for ASP programs with aggregates. Fundamenta Informaticae 107, 4, 379–413.Google Scholar
Faber, W., Pfeifer, G., and Leone, N. 2011. Semantics and complexity of recursive aggregates in answer set programming. Artificial Intelligence 175, 1, 278–298.Google Scholar
Faber, W., Pfeifer, G., Leone, N., Dell'Armi, T., and Ielpa, G. 2008. Design and implementation of aggregate functions in the DLV system. Theory and Practice of Logic Programming 8, 5–6, 545–580.Google Scholar
Ferraris, P. 2011. Logic programs with propositional connectives and aggregates. ACM Transactions on Computational Logic 12, 4, 25.Google Scholar
Ferraris, P. and Lifschitz, V. 2005. Weight constraints as nested expressions. Theory and Practice of Logic Programming 5, 1–2, 45–74.Google Scholar
Gebser, M., Harrison, A., Kaminski, R., Lifschitz, V., and Schaub, T. 2015. Abstract gringo. Theory and Practice of Logic Programming 15, 4–5, 449–463.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Romero, J., and Schaub, T. 2015. Progress in clasp Series 3. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 9345. Springer, 368–383.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., and Schaub, T. 2009. On the implementation of weight constraint rules in conflict-driven ASP solvers. In International Conference on Logic Programming. Lecture Notes in Computer Science, vol. 5649. Springer, 250–264.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. AAAI Press.Google Scholar
Gebser, M., Kaufmann, B., and Schaub, T. 2009. The conflict-driven answer set solver clasp: Progress report. In International Conference Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 5753. Springer, 509–514.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., Kaufmann, B., and Schaub, T. 2013. Advanced conflict-driven disjunctive answer set solving. In International Joint Conference on Artificial Intelligence. IJCAI/AAAI.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 Logic Programming. MIT Press, 1070–1080.Google Scholar
Gelfond, M. and Zhang, Y. 2014. Vicious circle principle and logic programs with aggregates. Theory and Practice of Logic Programming 14, 4–5, 587–601.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
Giunchiglia, E., Lierler, Y., and Maratea, M. 2006. Answer Set Programming Based on Propositional Satisfiability. Journal of Automated Reasoning 36, 4, 345–377.Google Scholar
Janhunen, T. 2006. Some (in)translatability results for normal logic programs and propositional theories. Journal of Applied Non-Classical Logics 16, 1–2, 35–86.Google Scholar
Janhunen, T. and Niemelä, I. 2016. The answer set programming paradigm. AI Magazine 37, 3, 13–24.Google Scholar
Lierler, Y. and Maratea, M. 2004. Cmodels-2: SAT-based Answer Set Solver Enhanced to Non-tight Programs. In International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Computer Science, vol. 2923. Springer, 346–350.Google Scholar
Lifschitz, V. 2016. Answer sets and the language of answer set programming. AI Magazine 37, 3, 7–12.Google Scholar
Liu, L., Pontelli, E., Son, T. C., and Truszczynski, M. 2010. Logic programs with abstract constraint atoms: The role of computations. Artificial Intelligence 174, 3–4, 295–315.Google Scholar
Nieuwenhuis, R., Oliveras, A., and Tinelli, C. 2006. Solving SAT and SAT Modulo Theories: From an abstract Davis–Putnam–Logemann–Loveland procedure to DPLL(T). Journal of the ACM 53, 6, 937–977.Google Scholar
Pelov, N., Denecker, M., and Bruynooghe, M. 2007. Well-founded and stable semantics of logic programs with aggregates. Theory and Practice of Logic Programming 7, 3, 301–353.Google Scholar
Simons, P., Niemelä, I., and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138, 1–2, 181–234.Google Scholar
Son, T. C. and Pontelli, E. 2007. A constructive semantic characterization of aggregates in answer set programming. Theory and Practice of Logic Programming 7, 3, 355–375.Google Scholar