Model Enumeration via Assumption Literals

• Autorzy: Alviano Mario , Dodaro Carmine

Identyfikatory

DOI

10.3233/FI-2019-1809

• Języki publikacji: EN

Abstrakty

EN

Modern, efficient Answer Set Programming solvers implement answer set search via non-chronological backtracking algorithms. The extension of these algorithms to answer set enumeration is nontrivial. In fact, adding blocking constraints to discard already computed answer sets is inadequate because the introduced constraints may not fit in memory or deteriorate the efficiency of the solver. On the other hand, the algorithm implemented by CLASP, which can run in polynomial space, requires to modify the answer set search procedure. The algorithm is revised in this paper so as to make it almost independent from the underlying answer set search procedure, provided that the procedure accepts as input a logic program and a list of assumption literals, and returns an answer set (and associated branching literals). In fact, thanks to an alternative view in terms of transition systems, the revised algorithm is suitable to easily accommodate the enumerate of models of other Boolean languages, among them classical models of propositional theories. On a pragmatic level, the paper presents two implementations of the enumeration algorithm, in WASP for answer set enumeration, and in GLUCOSE for classical models enumeration. The implemented systems are compared empirically to the state of the art solver CLASP.

Słowa kluczowe

EN

answer set programming; assumption literals; enumeration

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2019
• Tom: Vol. 167, nr 1-2
• Strony: 31--58
• Opis fizyczny: Bibliogr. 73 poz., tab., wykr.

Twórcy

autor

Alviano Mario

• Department of Mathematics and Computer Science, University of Calabria, via Pietro Bucci 30B, 87036 Rende (CS), Italy

autor

Dodaro Carmine

• Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, viale Francesco Causa 15, 16145 Genova (GE), Italy

Bibliografia

• [1] Gelfond M, Lifschitz V. Classical Negation in Logic Programs and Disjunctive Databases. New Generation Comput., 1991. 9(3/4):365-386. doi:10.1007/BF03037169.
• [2] Simons P, Niemelä I, Soininen T. Extending and implementing the stable model semantics. Artif. Intell., 2002. 138(1-2):181-234. doi:10.1016/S0004-3702(02)00187-X.
• [3] Alviano M, Faber W. The Complexity Boundary of Answer Set Programming with Generalized Atoms under the FLP Semantics. In: Cabalar P, Son TC (eds.), International Conference on Logic Programming and Nonmonotonic Reasoning, volume 8148 of Lecture Notes in Computer Science. Springer, 2013 pp.67-72. doi:10.1007/978-3-642-40564-8_7.
• [4] Alviano M, Faber W, Gebser M. Rewriting recursive aggregates in answer set programming: back to monotonicity. Theory and Practice of Logic Programming, 2015. 15(4-5):559-573. doi:10.1017/S1471068415000228.
• [5] Alviano M, Dodaro C. Anytime answer set optimization via unsatisfiable core shrinking. Theory and Practice of Logic Programming, 2016. 16(5-6):533-551. doi:10.1017/S147106841600020X.
• [6] Alviano M, Dodaro C, Ricca F. Anytime Computation of Cautious Consequences in Answer Set Programming. TPLP, 2014. 14(4-5):755-770. doi:10.1017/S1471068414000325.
• [7] Bliem B, Kaufmann B, Schaub T, Woltran S. ASP for Anytime Dynamic Programming on Tree Decompositions. In: Kambhampati S (ed.), Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI 2016, New York, NY, USA, 9-15 July 2016. IJCAI/AAAI Press, 2016 pp.979-986. URL http://www.ijcai.org/Abstract/16/143.
• [8] Davis M, Logemann G, Loveland DW. A machine program for theorem-proving. Commun. ACM, 1962. 5(7):394-397. doi:10.1145/368273.368557.
• [9] Brochenin R, Lierler Y, Maratea M. Abstract Disjunctive Answer Set Solvers. In: Schaub T, Friedrich G, O’Sullivan B (eds.), ECAI 2014 - 21st European Conference on Artificial Intelligence, 18-22 August 2014, Prague, Czech Republic - Including Prestigious Applications of Intelligent Systems (PAIS 2014), volume 263 of Frontiers in Artificial Intelligence and Applications. IOS Press, 2014 pp. 165-170. doi:10.3233/978-1-61499-419-0-165.
• [10] Giunchiglia E, Maratea M. On the Relation Between Answer Set and SAT Procedures (or, Between cmodels and smodels). In: Gabbrielli M, Gupta G (eds.), Logic Programming, 21st International Conference, ICLP 2005, Sitges, Spain, October 2-5, 2005, Proceedings, volume 3668 of Lecture Notes in Computer Science. Springer, 2005 pp. 37-51. doi:10.1007/11562931_6.
• [11] Leone N, Pfeifer G, Faber W, Eiter T, Gottlob G, Perri S, Scarcello F. The DLV system for knowledge representation and reasoning. ACM Trans. Comput. Log., 2006. 7(3):499-562. doi:10.1145/1149114.1149117.
• [12] Silva JPM, Sakallah KA. GRASP: A Search Algorithm for Propositional Satisfiability. IEEE Trans. Computers, 1999. 48(5):506-521. doi:10.1109/12.769433.
• [13] Zhang L, Madigan CF, Moskewicz MW, Malik S. Efficient Conflict Driven Learning in Boolean Satisfiability Solver. In: Ernst R (ed.), Proceedings of the 2001 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2001, San Jose, CA, USA, November 4-8, 2001. IEEE Computer Society, 2001 pp. 279-285. doi:10.1109/ICCAD.2001.968634.
• [14] Audemard G, Simon L. Refining Restarts Strategies for SAT and UNSAT. In: Milano M (ed.), Principles and Practice of Constraint Programming - 18th International Conference, CP 2012, Québec City, QC, Canada, October 8-12, 2012. Proceedings, volume 7514 of Lecture Notes in Computer Science. Springer, 2012 pp. 118-126. doi:10.1007/978-3-642-33558-7_11.
• [15] Gebser M, Kaufmann B, Neumann A, Schaub T. Conflict-Driven Answer Set Enumeration. In: Baral C, Brewka G, Schlipf JS (eds.), Logic Programming and Nonmonotonic Reasoning, 9th International Conference, LPNMR 2007, Tempe, AZ, USA, May 15-17, 2007, Proceedings, volume 4483 of Lecture Notes in Computer Science. Springer, 2007 pp. 136-148. doi:10.1007/978-3-540-72200-7_13.
• [16] Gebser M, Kaufmann B, Schaub T. Conflict-driven answer set solving: From theory to practice. Artificial Intelligence, 2012. 187:52-89. doi:10.1016/j.artint.2012.04.001.
• [17] Lierler Y. Abstract answer set solvers with backjumping and learning. TPLP, 2011. 11(2-3):135-169. doi:10.1017/S1471068410000578.
• [18] Lierler Y, Truszczynski M. Transition systems for model generators - A unifying approach. TPLP, 2011. 11(4-5):629-646. doi:10.1017/S1471068411000214.
• [19] Nieuwenhuis R, Oliveras A, Tinelli C. Solving SAT and SAT Modulo Theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM, 2006. 53(6):937-977. doi:10.1145/1217856.1217859.
• [20] Giunchiglia E, Lierler Y, Maratea M. Answer Set Programming Based on Propositional Satisfiability. J. Autom. Reasoning, 2006. 36(4):345-377. doi:10.1007/s10817-006-9033-2.
• [21] Janhunen T, Niemelä I. Compact Translations of Non-disjunctive Answer Set Programs to Propositional Clauses. In: Balduccini M, Son TC (eds.), Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning - Essays Dedicated to Michael Gelfond on the Occasion of His 65th Birthday, volume 6565 of Lecture Notes in Computer Science. Springer, 2011 pp. 111-130. doi:10.1007/978-3-642-20832-4_8.
• [22] Alviano M, Dodaro C. Answer Set Enumeration via Assumption Literals. In: Adorni G, Cagnoni S, Gori M, Maratea M (eds.), AI*IA 2016: Advances in Artificial Intelligence - XVth International Conference of the Italian Association for Artificial Intelligence, Genova, Italy, November 29 - December 1, 2016, Proceedings, volume 10037 of Lecture Notes in Computer Science. Springer, 2016 pp. 149-163. doi:10.1007/978-3-319-49130-1_12.
• [23] Alviano M, Dodaro C, Leone N, Ricca F. Advances in WASP. In: Calimeri F, Ianni G, Truszczynski M (eds.), International Conference on Logic Programming and Nonmonotonic Reasoning, volume 9345 of Lecture Notes in Computer Science. Springer, 2015 pp. 40-54. doi:10.1007/978-3-319-23264-5_5.
• [24] Audemard G, Simon L. Predicting Learnt Clauses Quality in Modern SAT Solvers. In: Boutilier C (ed.), IJCAI 2009, Proceedings of the 21st International Joint Conference on Artificial Intelligence, Pasadena, California, USA, July 11-17, 2009. 2009 pp. 399-404. URL http://ijcai.org/Proceedings/09/Papers/074.pdf.
• [25] Gebser M, Maratea M, Ricca F. What’s Hot in the Answer Set Programming Competition. In: Schuurmans D, Wellman MP (eds.), Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, February 12-17, 2016, Phoenix, Arizona, USA. AAAI Press, 2016 pp. 4327-4329. URL http://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12233.
• [26] Lierler Y, Maratea M, Ricca F. Systems, Engineering Environments, and Competitions. AI Magazine, 2016. 37(3):45-52. URL http://www.aaai.org/ojs/index.php/aimagazine/article/view/2675.
• [27] Gebser M, Maratea M, Ricca F. The Design of the Seventh Answer Set Programming Competition. In: Balduccini M, Janhunen T (eds.), Logic Programming and Nonmonotonic Reasoning - 14th International Conference, LPNMR 2017, Espoo, Finland, July 3-6, 2017, Proceedings, volume 10377 of Lecture Notes in Computer Science. Springer, 2017 pp. 3-9. doi:10.1007/978-3-319-61660-5_1.
• [28] Gebser M, Kaufmann B, Schaub T. Advanced Conflict-Driven Disjunctive Answer Set Solving. In: Rossi F (ed.), IJCAI 2013, Proceedings of the 23rd International Joint Conference on Artificial Intelligence, Beijing, China, August 3-9, 2013. IJCAI/AAAI, 2013 pp. 912-918. URL http://www.aaai.org/ocs/index.php/IJCAI/IJCAI13/paper/view/6835.
• [29] Koch C, Leone N, Pfeifer G. Enhancing disjunctive logic programming systems by SAT checkers. Artif. Intell., 2003. 151(1-2):177-212. doi:10.1016/S0004-3702(03)00078-X.
• [30] Dodaro C, Alviano M, Faber W, Leone N, Ricca F, Sirianni M. The Birth of a WASP: Preliminary Report on a New ASP Solver. In: Fioravanti F (ed.), Italian Conference on Computational Logic, volume 810 of CEUR Workshop Proceedings. CEUR-WS.org, 2011 pp. 99-113. URL http://ceur-ws.org/Vol-810/paper-l06.pdf.
• [31] Alviano M, Dodaro C, Faber W, Leone N, Ricca F. WASP: A Native ASP Solver Based on Constraint Learning. In: Cabalar P, Son TC (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, 2013 pp. 54-66. doi:10.1007/978-3-642-40564-8_6.
• [32] Gebser M, Kaminski R, Kaufmann B, Romero J, Schaub T. Progress in clasp Series 3. In: Calimeri F, Ianni G, Truszczynski M (eds.), Logic Programming and Nonmonotonic Reasoning - 13th International Conference, LPNMR 2015, Lexington, KY, USA, September 27-30, 2015. Proceedings, volume 9345 of Lecture Notes in Computer Science. Springer, 2015 pp. 368-383. doi:10.1007/978-3-319-23264-5_31.
• [33] Gebser M, Kaminski R, König A, Schaub T. Advances in gringo Series 3. In: Delgrande JP, Faber W (eds.), International Conference on Logic Programming and Nonmonotonic Reasoning, volume 6645 of Lecture Notes in Computer Science. Springer, 2011 pp. 345-351. doi:10.1007/978-3-642-20895-9_39.
• [34] Janhunen T. Some (in)translatability results for normal logic programs and propositional theories. Journal of Applied Non-Classical Logics, 2006. 16(1-2):35-86. doi:10.3166/jancl.16.35-86.
• [35] Bomanson J, Janhunen T. Normalizing Cardinality Rules Using Merging and Sorting Constructions. In: Cabalar P, Son TC (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, 2013 pp. 187-199. doi:10.1007/978-3-642-40564-8_19.
• [36] Öztok U, Erdem E. Generating Explanations for Complex Biomedical Queries. In: Burgard W, Roth D (eds.), Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2011, San Francisco, California, USA, August 7-11, 2011. AAAI Press, 2011 URL http://www.aaai.org/ocs/index.php/AAAI/AAAI11/paper/view/3519.
• [37] Baryannis G, Tachmazidis I, Batsakis S, Antoniou G, Alviano M, Sellis T, Tsai P. A Trajectory Calculus for Qualitative Spatial Reasoning Using Answer Set Programming. TPLP, 2018. 18(3-4):355-371. doi:10.1017/S147106841800011X.
• [38] Kaminski R, Schaub T, Siegel A, Videla S. Minimal intervention strategies in logical signaling networks with ASP. TPLP, 2013. 13(4-5):675-690. doi:10.1017/S1471068413000422.
• [39] Erdem E, Gelfond M, Leone N. Applications of Answer Set Programming. AI Magazine, 2016. 37(3):53-68. URL http://www.aaai.org/ojs/index.php/aimagazine/article/view/2678.
• [40] Alviano M, Faber W, Leone N, Perri S, Pfeifer G, Terracina G. The Disjunctive Datalog System DLV. In: de Moor O, Gottlob G, Furche T, Sellers AJ (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, 2010 pp. 282-301. doi:10.1007/978-3-642-24206-9_17.
• [41] Maratea M, Ricca F, Faber W, Leone N. Look-back techniques and heuristics in DLV: Implementation, evaluation, and comparison to QBF solvers. J. Algorithms, 2008. 63(1-3):70-89. doi:10.1016/j.jalgor.2008.02.006.
• [42] Adrian WT, Alviano M, Calimeri F, Cuteri B, Dodaro C, Faber W, Fuscà D, Leone N, Manna M, Perri S, Ricca F, Veltri P, Zangari J. The ASP System DLV: Advancements and Applications. KI, 2018. 32(2-3):177-179. doi:10.1007/s13218-018-0533-0.
• [43] Syrjänen T, Niemelä I. The Smodels System. In: Eiter T, Faber W, Truszczynski M (eds.), Logic Programming and Nonmonotonic Reasoning, 6th International Conference, LPNMR 2001, Vienna, Austria, September 17-19, 2001, Proceedings, volume 2173 of Lecture Notes in Computer Science. Springer, 2001 pp. 434-438. doi:10.1007/3-540-45402-0_38.
• [44] Niemelä I, Simons P. Smodels - An Implementation of the Stable Model and Well-Founded Semantics for Normal LP. In: Dix J, Furbach U, Nerode A (eds.), Logic Programming and Nonmonotonic Reasoning, 4th International Conference, LPNMR’97, Dagstuhl Castle, Germany, July 28-31, 1997, Proceedings, volume 1265 of Lecture Notes in Computer Science. Springer, 1997 pp. 421-430. doi:10.1007/3-540-63255-7_32.
• [45] Giunchiglia E, Leone N, Maratea M. On the relation among answer set solvers. Ann. Math. Artif. Intell., 2008. 53(1-4):169-204. doi:10.1007/s10472-009-9113-1.
• [46] Lierler Y, Maratea M. Cmodels-2: SAT-based Answer Set Solver Enhanced to Non-tight Programs. In: Lifschitz V, 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, 2004 pp. 346-350. doi:10.1007/978-3-540-24609-1_32.
• [47] Giunchiglia E, Lierler Y, Maratea M. SAT-Based Answer Set Programming. In: McGuinness DL, Ferguson G (eds.), Proceedings of the Nineteenth National Conference on Artificial Intelligence, Sixteenth Conference on Innovative Applications of Artificial Intelligence, July 25-29, 2004, San Jose, California, USA. AAAI Press / The MIT Press, 2004 pp. 61-66. URL http://www.aaai.org/Library/AAAI/2004/aaai04-010.php.
• [48] Bruynooghe M, Blockeel H, Bogaerts B, Cat BD, Pooter SD, Jansen J, Labarre A, Ramon J, Denecker M, Verwer S. Predicate logic as a modeling language: modeling and solving some machine learning and data mining problems with IDP3. TPLP, 2015. 15(6):783-817. doi:10.1017/S147106841400009X.
• [49] Denecker M, Ternovska E. A logic of nonmonotone inductive definitions. ACM Trans. Comput. Log., 2008. 9(2):14:1-14:52. doi:10.1145/1342991.1342998.
• [50] Biere A. Lingeling Essentials, A Tutorial on Design and Implementation Aspects of the the SAT Solver Lingeling. In: Berre DL (ed.), POS-14. Fifth Pragmatics of SAT workshop, a workshop of the SAT 2014 conference, part of FLoC 2014 during the Vienna Summer of Logic, July 13, 2014, Vienna, Austria, volume 27 of EPiC Series in Computing. EasyChair, 2014 p. 88. URL http://www.easychair.org/publications/paper/182026.
• [51] Jabbour S, Lonlac J, Sais L, Salhi Y. Extending modern SAT solvers for models enumeration. In: Joshi J, Bertino E, Thuraisingham BM, Liu L (eds.), Proceedings of the 15th IEEE International Conference on Information Reuse and Integration, IRI 2014, Redwood City, CA, USA, August 13-15, 2014. IEEE Computer Society, 2014 pp. 803-810. doi:10.1109/IRI.2014.7051971.
• [52] Alviano M, Faber W. Stable Model Semantics of Abstract Dialectical Frameworks Revisited: A Logic Programming Perspective. In: Yang Q, Wooldridge M (eds.), Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015. AAAI Press, 2015 pp. 2684-2690. URL http://ijcai.org/Abstract/15/380.
• [53] Brewka G, Strass H, Ellmauthaler S, Wallner JP, Woltran S. Abstract Dialectical Frameworks Revisited. In: Rossi F (ed.), IJCAI 2013, Proceedings of the 23rd International Joint Conference on Artificial Intelligence, Beijing, China, August 3-9, 2013. IJCAI/AAAI, 2013 pp. 803-809. URL http://www.aaai.org/ocs/index.php/IJCAI/IJCAI13/paper/view/6551.
• [54] Brewka G, Woltran S. Abstract Dialectical Frameworks. In: Lin F, Sattler U, Truszczynski M (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Twelfth International Conference, KR 2010, Toronto, Ontario, Canada, May 9-13, 2010. AAAI Press, 2010 URL http://aaai.org/ocs/index.php/KR/KR2010/paper/view/1294.
• [55] Bistarelli S, Rossi F, Santini F. A Comparative Test on the Enumeration of Extensions in Abstract Argumentation. Fundam. Inform., 2015. 140(3-4):263-278. doi:10.3233/FI-2015-1254.
• [56] Thimm M, Villata S, Cerutti F, Oren N, Strass H, Vallati M. Summary Report of The First International Competition on Computational Models of Argumentation. AI Magazine, 2016. 37(1):102. URL http://www.aaai.org/ojs/index.php/aimagazine/article/view/2640.
• [57] Alviano M. The Ingredients of the Argumentation Reasoner pyglaf: Python, Circumscription, and Glucose to Taste. In: Maratea M, Serina I (eds.), Proceedings of the 24th RCRA International Workshop on Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion 2017 colocated with the 16th International Conference of the Italian Association for Artificial Intelligence (AI*IA 2017), Bari, Italy, November 14-15, 2017., volume 2011 of CEUR Workshop Proceedings. CEUR-WS.org, 2017 pp. 1-16. URL http://ceur-ws.org/Vol-2011/paper1.pdf.
• [58] Alviano M. The Pyglaf Argumentation Reasoner. In: Rocha R, Son TC, Mears C, Saeedloei N (eds.), Technical Communications of the 33rd International Conference on Logic Programming, ICLP 2017, August 28 to September 1, 2017, Melbourne, Australia, volume 58 of OASICS. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017 pp. 2:1-2:3. doi:10.4230/OASIcs.ICLP.2017.2.
• [59] Alviano M. Model enumeration in propositional circumscription via unsatisfiable core analysis. TPLP, 2017. 17(5-6):708-725. doi:10.1017/S1471068417000278.
• [60] Alviano M. Query Answering in Propositional Circumscription. In: Lang J (ed.), Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, July 13-19, 2018, Stockholm, Sweden. ijcai.org, 2018 pp. 1669-1675. doi:10.24963/ijcai.2018/231.
• [61] Brewka G, Delgrande JP, Romero J, Schaub T. Implementing Preferences with asprin. In: Calimeri F, Ianni G, Truszczynski M (eds.), Logic Programming and Nonmonotonic Reasoning - 13th International Conference, LPNMR 2015, Lexington, KY, USA, September 27-30, 2015. Proceedings, volume 9345 of Lecture Notes in Computer Science. Springer, 2015 pp. 158-172. doi:10.1007/978-3-319-23264-5_15.
• [62] Brewka G, Delgrande JP, Romero J, Schaub T. asprin: Customizing Answer Set Preferences without a Headache. In: Bonet B, Koenig S (eds.), Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, January 25-30, 2015, Austin, Texas, USA. AAAI Press, 2015 pp. 1467-1474. URL http://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/view/9535.
• [63] Alviano M, Romero J, Schaub T. Preference Relations by Approximation. In: Thielscher M, Toni F, Wolter F (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, Tempe, Arizona, 30 October - 2 November 2018. AAAI Press, 2018 pp. 2-11. URL https://aaai.org/ocs/index.php/KR/KR18/paper/view/18001.
• [64] Brochenin R, Maratea M, Lierler Y. Disjunctive answer set solvers via templates. TPLP, 2016. 16(4):465-497. doi:10.1017/S1471068415000411.
• [65] Brochenin R, Maratea M. Abstract Solvers for Quantified Boolean Formulas and their Applications. In: Gavanelli M, Lamma E, Riguzzi F (eds.), International Conference of the Italian Association for Artificial Intelligence, volume 9336 of Lecture Notes in Computer Science. Springer, 2015 pp. 205-217. doi:10.1007/978-3-319-24309-2_16.
• [66] Alviano M, Leone N. Complexity and compilation of GZ-aggregates in answer set programming. Theory and Practice of Logic Programming, 2015. 15(4-5):574-587. doi:10.1017/S147106841500023X.
• [67] Faber W, Pfeifer G, Leone N. Semantics and complexity of recursive aggregates in answer set programming. Artificial Intelligence, 2011. 175(1):278-298. doi:10.1016/j.artint.2010.04.002.
• [68] Alviano M, Dodaro C, Maratea M. Shared aggregate sets in answer set programming. TPLP, 2018. 18(3-4):301-318. doi:10.1017/S1471068418000133.
• [69] Alviano M, Dodaro C. Unsatisfiable Core Shrinking for Anytime Answer Set Optimization. In: Sierra C (ed.), Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017. ijcai.org, 2017 pp. 4781-4785. doi:10.24963/ijcai.2017/666.
• [70] Alviano M, Dodaro C, Marques-Silva J, Ricca F. Optimum stable model search: algorithms and implementation. Journal of Logic and Computation, 2015. doi:10.1093/logcom/exv061.
• [71] Alviano M, Dodaro C, Ricca F. A MaxSAT Algorithm Using Cardinality Constraints of Bounded Size. In: Yang Q, Wooldridge M (eds.), Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015. AAAI Press, 2015 pp.2677-2683. URL http://ijcai.org/Abstract/15/379.
• [72] Alviano M, Dodaro C, Järvisalo M, Maratea M, Previti A. Cautious reasoning in ASP via minimal models and unsatisfiable cores. TPLP, 2018. 18(3-4):319-336. doi:10.1017/S1471068418000145.
• [73] Brochenin R, Maratea M. Abstract Answer Set Solvers for Cautious Reasoning. In: Vos MD, Eiter T, Lierler Y, Toni F (eds.), Proceedings of the Technical Communications of the 31st International Conference on Logic Programming (ICLP 2015), Cork, Ireland, August 31 - September 4, 2015., volume 1433 of CEUR Workshop Proceedings. CEUR-WS.org, 2015 URL http://ceur-ws.org/Vol-1433/tc_48.pdf.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).