Skip to main content Accessibility help
×
Home

Anytime answer set optimization via unsatisfiable core shrinking

Published online by Cambridge University Press:  14 October 2016


MARIO ALVIANO
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, Italy (e-mail: alviano@mat.unical.it, dodaro@mat.unical.it)
CARMINE DODARO
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, Italy (e-mail: alviano@mat.unical.it, dodaro@mat.unical.it)
Corresponding

Abstract

Unsatisfiable core analysis can boost the computation of optimum stable models for logic programs with weak constraints. However, current solvers employing unsatisfiable core analysis either run to completion, or provide no suboptimal stable models but the one resulting from the preliminary disjoint cores analysis. This drawback is circumvented here by introducing a progression based shrinking of the analyzed unsatisfiable cores. In fact, suboptimal stable models are possibly found while shrinking unsatisfiable cores, hence resulting into an anytime algorithm. Moreover, as confirmed empirically, unsatisfiable core analysis also benefits from the shrinking process in terms of solved instances.


Type
Regular Papers
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below.

References

Alviano, M., Dodaro, C., Faber, W., Leone, N. and Ricca, F. 2013. WASP: A native ASP solver based on constraint learning. In Cabalar, P. and Son, T. C. (Eds.), Logic Programming and Nonmonotonic Reasoning, 12th International Conference, LPNMR 2013, Corunna, Spain, September 15-19, 2013. Proceedings, Volume 8148 of Lecture Notes in Computer Science, Springer, 5466.Google Scholar
Alviano, M., Dodaro, C., Leone, N. and Ricca, F. 2015a. Advances in WASP. In Calimeri, F., Ianni, G. and Truszczynski, M. (Eds.), Proceedings of Logic Programming and Nonmonotonic Reasoning - 13th International Conference, LPNMR 2015, Volume 9345 of Lecture Notes in Computer Science, Springer, 4054.Google Scholar
Alviano, M., Dodaro, C., Marques-Silva, J. and Ricca, F. 2015b. Optimum stable model search: algorithms and implementation. Journal of Logic and Computation.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, 755770.CrossRefGoogle Scholar
Alviano, M., Dodaro, C. and Ricca, F. 2015c. A MaxSAT Algorithm Using Cardinality Constraints of Bounded Size. In Yang, Q. and Wooldridge, M. (Eds.), Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, AAAI Press, 26772683.Google Scholar
Alviano, M. and Faber, W. 2013. The complexity boundary of answer set programming with generalized atoms under the FLP semantics. In Cabalar, P. and Son, T. C. (Eds.), Logic Programming and Nonmonotonic Reasoning, 12th International Conference, LPNMR 2013, Corunna, Spain, September 15-19, 2013. Proceedings, Volume 8148 of Lecture Notes in Computer Science, Springer, 6772.Google Scholar
Alviano, M., Faber, W. and Gebser, M. 2015d. Rewriting recursive aggregates in answer set programming: back to monotonicity. Theory and Practice of Logic Programming 15, 4–5, 559573.CrossRefGoogle Scholar
Alviano, M., Faber, W., Leone, N., Perri, S., Pfeifer, G. and Terracina, G. 2010. The disjunctive datalog system DLV. In de Moor, O., Gottlob, G., Furche, T. and Sellers, A. J. (Eds.), Datalog Reloaded - First International Workshop, Datalog 2010, Oxford, UK, March 16-19, 2010. Revised Selected Papers, Volume 6702 of Lecture Notes in Computer Science, Springer, 282301.Google Scholar
Alviano, M., Faber, W. and Strass, H. 2016. Boolean functions with ordered domains in answer set programming. In Schuurmans, D. and Wellman, M. P. (Eds.), Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, February 12-17, 2016, Phoenix, Arizona, USA., AAAI Press, 879885.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, 574587.CrossRefGoogle Scholar
Andres, B., Kaufmann, B., Matheis, O. and Schaub, T. 2012. Unsatisfiability-based optimization in clasp. In Dovier, A. and Costa, V. S. (Eds.), Technical Communications of the 28th International Conference on Logic Programming, ICLP 2012, Volume 17 of LIPIcs, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 211–221.Google Scholar
Ansótegui, C., Bonet, M. L. and Levy, J. 2009. Solving (weighted) partial maxsat through satisfiability testing. In Kullmann, O. (Ed.), Proceedings of Theory and Applications of Satisfiability Testing, SAT 2009, Volume 5584 of Lecture Notes in Computer Science, Springer, 427–440.Google Scholar
Argelich, J., Lynce, I. and Silva, J. P. M. 2009. On Solving Boolean Multilevel Optimization Problems. In Boutilier, C. (Ed.), Proceedings of the 21st International Joint Conference on Artificial Intelligence, IJCAI 2009, 393–398.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, Papers from the 2011 AAAI Spring Symposium, Technical Report SS-11-06, Stanford, California, USA, March 21-23, 2011. AAAI.Google Scholar
Bliem, B., Kaufmann, B., Schaub, T. and Woltran, S. 2016. ASP for Anytime Dynamic Programming on Tree Decompositions. In Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI 2016. AAAI Press.Google Scholar
Brewka, G., Eiter, T. and Truszczynski, M. 2011. Answer set programming at a glance. Commun. ACM 54, 12, 92103.CrossRefGoogle Scholar
Buccafurri, F., Leone, N. and Rullo, P. 2000. Enhancing Disjunctive Datalog by Constraints. IEEE Trans. Knowl. Data Eng. 12, 5, 845860.CrossRefGoogle Scholar
Cha, B., Iwama, K., Kambayashi, Y. and Miyazaki, S. 1997. Local search algorithms for partial MAXSAT. In Fourteenth National Conference on Artificial Intelligence and Ninth Innovative Applications of Artificial Intelligence Conference, AAAI Press / The MIT Press, 263268.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 Fioravanti, F. (Ed.), Proceedings of the 26th Italian Conference on Computational Logic, Pescara, Italy, August 31 - September 2, 2011, Volume 810 of CEUR Workshop Proceedings, CEUR-WS.org, 99–113.Google Scholar
Eiter, T., Ianni, G. and Krennwallner, T. 2009. Answer Set Programming: A Primer. In Tessaris, S., Franconi, E., Eiter, T., Gutierrez, C., Handschuh, S., Rousset, M. and Schmidt, R. A. (Eds.), Reasoning Web. Semantic Technologies for Information Systems, 5th International Summer School 2009, Tutorial Lectures, Volume 5689 of Lecture Notes in Computer Science, Springer, 40110.Google Scholar
Faber, W., Pfeifer, G. and Leone, N. 2011. Semantics and complexity of recursive aggregates in answer set programming. Artif. Intell. 175, 1, 278298.CrossRefGoogle Scholar
Ferraris, P. 2011. Logic programs with propositional connectives and aggregates. ACM Trans. Comput. Log. 12, 4, 25.CrossRefGoogle Scholar
Fu, Z. and Malik, S. 2006. On Solving the Partial MAX-SAT Problem. In Biere, A. and Gomes, C. P. (Eds.), Proceedings of Theory and Applications of Satisfiability Testing, SAT 2006, Volume 4121 of Lecture Notes in Computer Science, Springer, 252265.CrossRefGoogle Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Romero, J. and Schaub, T. 2015a. Progress in clasp Series 3. In Calimeri, F., Ianni, G. and Truszczynski, M. (Eds.), LPNMR 2015, Volume 9345 of Lecture Notes in Computer Science, Springer, 368383.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2011a. Multi-Criteria Optimization in Answer Set Programming. In Gallagher, J. P. and Gelfond, M. (Eds.), Technical Communications of the 27th International Conference on Logic Programming, ICLP 2011, Volume 11 of LIPIcs, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 1–10.Google Scholar
Gebser, M., Kaminski, R. and Schaub, T. 2011b. Complex optimization in answer set programming. Theory and Practice of Logic Programming 11, 4–5, 821839.CrossRefGoogle Scholar
Gebser, M., Maratea, M. and Ricca, F. 2015b. The Design of the Sixth Answer Set Programming Competition. In Calimeri, F., Ianni, G. and Truszczynski, M. (Eds.), Proceedings of Logic Programming and Nonmonotonic Reasoning - 13th International Conference, LPNMR 2015, Volume 9345 of Lecture Notes in Computer Science, Springer, 531544.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical Negation in Logic Programs and Disjunctive Databases. New Generation Comput. 9, 3/4, 365386.CrossRefGoogle Scholar
Gelfond, M. and Zhang, Y. 2014. Vicious circle principle and logic programs with aggregates. Theory and Practice of Logic Programming 14, 4–5, 587601.CrossRefGoogle Scholar
Giunchiglia, E., Lierler, Y. and Maratea, M. 2006. Answer set programming based on propositional satisfiability. J. Autom. Reasoning 36, 4, 345377.CrossRefGoogle Scholar
Lierler, Y. and Maratea, M. 2004. Cmodels-2: Sat-based answer set solver enhanced to non-tight programs. In Lifschitz, V. and Niemelä, I. (Eds.), Logic Programming and Nonmonotonic Reasoning, 7th International Conference, LPNMR 2004, Fort Lauderdale, FL, USA, January 6-8, 2004, Proceedings, Volume 2923 of Lecture Notes in Computer Science, Springer, 346350.Google Scholar
Lifschitz, V. 2008. What Is Answer Set Programming? In Fox, D. and Gomes, C. P. (Eds.), Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, AAAI Press, 15941597.Google Scholar
Liu, G., Janhunen, T. and Niemelä, I. 2012. Answer Set Programming via Mixed Integer Programming. In Brewka, G., Eiter, T. and McIlraith, S. A. (Eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Thirteenth International Conference, KR 2012. AAAI Press.Google Scholar
Liu, L., Pontelli, E., Son, T. C. and Truszczynski, M. 2010. Logic programs with abstract constraint atoms: The role of computations. Artif. Intell. 174, 3–4, 295315.CrossRefGoogle Scholar
Manquinho, V. M., Silva, J. P. M. and Planes, J. 2009. Algorithms for weighted boolean optimization. In Kullmann, O. (Ed.), Proceedings of Theory and Applications of Satisfiability Testing, SAT 2009, Volume 5584 of Lecture Notes in Computer Science, Springer, 495508.CrossRefGoogle Scholar
Marek, V. W., Niemelä, I. and Truszczynski, M. 2008. Logic programs with monotone abstract constraint atoms. Theory and Practice of Logic Programming 8, 2, 167199.CrossRefGoogle Scholar
Marques-Silva, J. and Manquinho, V. M. 2008. Towards more effective unsatisfiability-based maximum satisfiability algorithms. In Büning, H. K. and Zhao, X. (Eds.), Proceedings of Theory and Applications of Satisfiability Testing, SAT 2008, Volume 4996 of Lecture Notes in Computer Science, Springer, 225230.CrossRefGoogle Scholar
Marques-Silva, J. and Planes, J. 2008. Algorithms for Maximum Satisfiability using Unsatisfiable Cores. In Design, Automation and Test in Europe, DATE 2008, Munich, Germany, IEEE, 408413.CrossRefGoogle Scholar
Morgado, A., Dodaro, C. and Marques-Silva, J. 2014. Core-Guided MaxSAT with Soft Cardinality Constraints. In Proceedings of Principles and Practice of Constraint Programming - 20th International Conference, CP 2014, Lyon, France, Springer, 564573.Google Scholar
Nadel, A. 2010. Boosting minimal unsatisfiable core extraction. In Bloem, R. and Sharygina, N. (Eds.), Proceedings of 10th International Conference on Formal Methods in Computer-Aided Design, FMCAD 2010, IEEE, 221229.Google Scholar
Nadel, A., Ryvchin, V. and Strichman, O. 2014. Accelerated Deletion-based Extraction of Minimal Unsatisfiable Cores. JSAT 9, 2751.Google Scholar
Narodytska, N. and Bacchus, F. 2014. Maximum Satisfiability Using Core-Guided MaxSAT Resolution. In Twenty-Eighth AAAI Conference on Artificial Intelligence, Québec City, Canada, AAAI Press, 27172723.Google Scholar
Niemelä, I. 1999. Logic Programs with Stable Model Semantics as a Constraint Programming Paradigm. Ann. Math. Artif. Intell. 25, 3–4, 241273.CrossRefGoogle Scholar
Simons, P., Niemelä, I. and Soininen, T. 2002. Extending and implementing the stable model semantics. Artif. Intell. 138, 1–2, 181234.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 88 *
View data table for this chart

* Views captured on Cambridge Core between 14th October 2016 - 2nd December 2020. This data will be updated every 24 hours.

Hostname: page-component-79f79cbf67-hdh2x Total loading time: 0.665 Render date: 2020-12-02T02:35:15.091Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags last update: Wed Dec 02 2020 02:06:04 GMT+0000 (Coordinated Universal Time) Feature Flags: { "metrics": true, "metricsAbstractViews": false, "peerReview": true, "crossMark": true, "comments": true, "relatedCommentaries": true, "subject": true, "clr": false, "languageSwitch": true }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Anytime answer set optimization via unsatisfiable core shrinking
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Anytime answer set optimization via unsatisfiable core shrinking
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Anytime answer set optimization via unsatisfiable core shrinking
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *