{"type":"ScholarlyArticle","title":"Simulating Sets in Answer Set Programming","authors":[{"name":"Sarah Alice Gaggl","slug":"sarah-alice-gaggl","given":"Sarah Alice","family":"Gaggl","affiliation":"Logic Programming and Argumentation Group , TU Dresden , Germany"},{"name":"Philipp Hanisch","slug":"philipp-hanisch","given":"Philipp","family":"Hanisch","affiliation":"Knowledge-Based Systems Group , TU Dresden , Germany"},{"name":"Markus Krötzsch","slug":"markus-krotzsch","given":"Markus","family":"Krötzsch","affiliation":"Knowledge-Based Systems Group , TU Dresden , Germany"}],"abstract":"We study the extension of non-monotonic disjunctive logic programs with terms that represent sets of constants, called DLP(S), under the stable model semantics. This strictly increases expressive power, but keeps reasoning decidable, though cautious entailment is coNEXPTIME^NP-complete, even for data complexity. We present two new reasoning methods for DLP(S): a semantics-preserving translation of DLP(S) to logic programming with function symbols, which can take advantage of lazy grounding techniques, and a ground-and-solve approach that uses non-monotonic existential rules in the grounding stage. Our evaluation considers problems of ontological reasoning that are not in scope for traditional ASP (unless EXPTIME =ΠP2 ), and we find that our new existential-rule grounding performs well in comparison with native implementations of set terms in ASP.","doi":"10.24963/ijcai.2022/365","url":"https://ijcai.org/proceedings/2022/365","pdf":"https://ijcai.org/proceedings/2022/0365.pdf","markdown":"https://ijcai.org/proceedings/2022/365.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/365","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":365,"pages":{"first":2634,"last":2640},"keywords":["Knowledge Representation and Reasoning: Logic Programming","Knowledge Representation and Reasoning: Non-monotonic Reasoning","Knowledge Representation and Reasoning: Computational Complexity of Reasoning"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38987090","length_sec":115,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985233","length_sec":690,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Bonatti, 2004] Piero A. Bonatti. Reasoning with infinite sta- ble models. Artif. Intell., 156(1):75-111, 2004.","title":"Reasoning with infinite stable models","authors":"A Piero, Bonatti","year":"2004","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Brewka et al., 2011] Gerhard Brewka, Thomas Eiter, and Miroslaw Truszczynski. Answer set programming at a glance. Commun. ACM, 54(12):92-103, 2011.","title":"Answer set programming at a glance","authors":"Gerhard Brewka, Thomas Eiter, Miroslaw Truszczynski","year":"2011","venue":"Commun. ACM","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Calimeri et al., 2008] Francesco Calimeri, Susanna Cozza, Giovambattista Ianni, and Nicola Leone. Computable functions in ASP: theory and implementation. In Proc. 24th Int. Conf. on Logic Programming (ICLP'08), volume 5366 of LNCS, pages 407-424. Springer, 2008.","title":"Computable functions in ASP: theory and implementation","authors":"Francesco Calimeri, Susanna Cozza, Giovambattista Ianni, Nicola Leone","year":"2008","venue":"Proc. 24th Int. Conf. on Logic Programming (ICLP'08)","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Calimeri et al., 2009] Francesco Calimeri, Susanna Cozza, Giovambattista Ianni, and Nicola Leone. An ASP sys- tem with functions, lists, and sets. In Proc. 10th Int. Conf. on Logic Programming and Nonmonotonic Reason- ing (LPNMR'09), volume 5753 of LNCS, pages 483-489. Springer, 2009.","title":"An ASP system with functions, lists, and sets","authors":"Francesco Calimeri, Susanna Cozza, Giovambattista Ianni, Nicola Leone","year":"2009","venue":"Proc. 10th Int. Conf. on Logic Programming and Nonmonotonic Reasoning (LPNMR'09)","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Carral et al., 2019a] David Carral, Irina Dragoste, Larry González, Ceriel Jacobs, Markus Krötzsch, and Jacopo Ur- bani. VLog: A rule engine for knowledge graphs. In Proc. 18th Int. Semantic Web Conf. (ISWC'19, Part II), volume 11779 of LNCS, pages 19-35. Springer, 2019.","title":"VLog: A rule engine for knowledge graphs","authors":"Carral","year":"2019","venue":"Proc. 18th Int. Semantic Web Conf. (ISWC'19, Part II)","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Carral et al., 2019b] David Carral, Irina Dragoste, Markus Krötzsch, and Christian Lewe. Chasing sets: How to use existential rules for expressive reasoning. In Proc. 28th Int. Joint Conf. on Artificial Intelligence (IJCAI'19), pages 1624-1631. ijcai.org, 2019.","title":"Chasing sets: How to use existential rules for expressive reasoning","authors":"Carral","year":"2019","venue":"Proc. 28th Int. Joint Conf. on Artificial Intelligence (IJCAI'19)","doi":null,"url":null,"internal_url":"/proceedings/2019/225"},{"position":7,"raw":"[Dantsin et al., 2001] Evgeny Dantsin, Thomas Eiter, Georg Gottlob, and Andrei Voronkov. Complexity and expressive power of logic programming. ACM Computing Surveys, 33(3):374-425, 2001.","title":"Complexity and expressive power of logic programming","authors":"Evgeny Dantsin, Thomas Eiter, Georg Gottlob, Andrei Voronkov","year":"2001","venue":"ACM Computing Surveys","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Eiter and Simkus, 2010] Thomas Eiter and Mantas Simkus. FDNC: decidable nonmonotonic disjunctive logic pro- grams with function symbols. ACM Trans. Comput. Log., 11(2):14:1-14:50, 2010.","title":"FDNC: decidable nonmonotonic disjunctive logic programs with function symbols","authors":"Thomas Eiter, Mantas Simkus","year":"2010","venue":"ACM Trans. Comput. Log","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Eiter et al., 2004] Thomas Eiter, Thomas Lukasiewicz, Ro- man Schindlauer, and Hans Tompits. Combining answer set programming with description logics for the Semantic Web. In Proc. 9th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'04), pages 141-151. AAAI Press, 2004.","title":"Combining answer set programming with description logics for the Semantic Web","authors":"Thomas Eiter, Thomas Lukasiewicz, Roman Schindlauer, Hans Tompits","year":"2004","venue":"Proc. 9th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'04)","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Faber, 2020] Wolfgang Faber. An introduction to answer set programming and some of its extensions. In Tutorial Lec- tures 16th Int. Summer School on Reasoning Web. Declar- ative Artificial Intelligence, volume 12258 of LNCS, pages 149-185. Springer, 2020.","title":"An introduction to answer set programming and some of its extensions","authors":"Wolfgang Faber, Faber","year":"2020","venue":"Tutorial Lectures 16th Int. Summer School on Reasoning Web. Declarative Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Gaggl et al., 2015] Sarah Alice Gaggl, Norbert Manthey, Alessandro Ronca, Johannes Peter Wallner, and Stefan Woltran. Improved answer-set programming encodings for abstract argumentation. Theory Pract. Log. Program., 15(4-5):434-448, 2015.","title":"Improved answer-set programming encodings for abstract argumentation","authors":"Alice Sarah, Norbert Gaggl, Alessandro Manthey, Johannes Ronca, Stefan Peter Wallner, Woltran","year":"2015","venue":"Theory Pract. Log. Program","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Gebser et al., 2007] Martin Gebser, Benjamin Kaufmann, André Neumann, and Torsten Schaub. clasp: A conflict- driven answer set solver. In LPNMR, volume 4483 of Lec- ture Notes in Computer Science, pages 260-265. Springer, 2007.","title":"clasp: A conflictdriven answer set solver","authors":"Martin Gebser, Benjamin Kaufmann, André Neumann, Torsten Schaub","year":"2007","venue":"LPNMR","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Gebser et al., 2018] Martin Gebser, Nicola Leone, Marco Maratea, Simona Perri, Francesco Ricca, and Torsten Schaub. Evaluation techniques and systems for answer set programming: a survey. In Proc. 27th Int. Conf. on Artifi- cial Intelligence, (IJCAI'18), pages 5450-5456. ijcai.org, 2018.","title":"Evaluation techniques and systems for answer set programming: a survey","authors":"Martin Gebser, Nicola Leone, Marco Maratea, Simona Perri, Francesco Ricca, Torsten Schaub","year":"2018","venue":"Proc. 27th Int. Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2018/769"},{"position":14,"raw":"[Krötzsch et al., 2019] Markus Krötzsch, Maximilian Marx, and Sebastian Rudolph. The power of the terminating chase. In Proc. 22nd Int. Conf. on Database Theory (ICDT'19), volume 127 of LIPIcs, pages 3:1-3:17. Schloss Dagstuhl -Leibniz-Zentrum fuer Informatik, 2019.","title":"The power of the terminating chase","authors":"Krötzsch","year":"2019","venue":"Proc. 22nd Int. Conf. on Database Theory (ICDT'19)","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Lefèvre et al., 2017] Claire Lefèvre, Christopher Béatrix, Igor Stéphan, and Laurent Garcia. Asperix, a first-order forward chaining approach for answer set computing. The- ory Pract. Log. Program., 17(3):266-310, 2017.","title":"Asperix, a first-order forward chaining approach for answer set computing","authors":"Claire Lefèvre, Christopher Béatrix, Igor Stéphan, Laurent Garcia","year":"2017","venue":"Theory Pract. Log. Program","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Lifschitz and Turner, 1994] Vladimir Lifschitz and Hudson Turner. Splitting a logic program. In Proc. 11th Int. Conf. on Logic Programming (ICLP'94), pages 23-37. MIT Press, 1994.","title":"Splitting a logic program","authors":"Turner ; Lifschitz, Vladimir Lifschitz, Hudson Turner","year":"1994","venue":"Proc. 11th Int. Conf. on Logic Programming (ICLP'94)","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Lifschitz, 2019] Vladimir Lifschitz. Answer Set Program- ming. Springer, 2019.","title":"Answer Set Programming","authors":"Vladimir Lifschitz","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Ortiz et al., 2010] Magdalena Ortiz, Sebastian Rudolph, and Mantas Simkus. Worst-case optimal reasoning for the Horn-DL fragments of OWL 1 and 2. In Proc. 12th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'10), pages 269-279. AAAI Press, 2010.","title":"Worst-case optimal reasoning for the Horn-DL fragments of OWL 1 and 2","authors":"Magdalena Ortiz, Sebastian Rudolph, Mantas Simkus","year":"2010","venue":"Proc. 12th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'10)","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Taupe et al., 2019] Richard Taupe, Antonius Weinzierl, and Gerhard Friedrich. Degrees of laziness in grounding -ef- fects of lazy-grounding strategies on ASP solving. In Proc. 15th Int. Conf. on Logic Programming and Nonmonotonic Reasoning (LPNMR'19), volume 11481 of LNCS, pages 298-311. Springer, 2019.","title":"Degrees of laziness in grounding -effects of lazy-grounding strategies on ASP solving","authors":"Richard Taupe, Antonius Weinzierl, Gerhard Friedrich","year":"2019","venue":"Proc. 15th Int. Conf. on Logic Programming and Nonmonotonic Reasoning (LPNMR'19)","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Weinzierl, 2017] Antonius Weinzierl. Blending lazy- grounding and CDNL search for answer-set solving. In Proc. 14th Int. Conf. on Logic Programming and Non- monotonic Reasoning (LPNMR'17), volume 10377 of LNCS, pages 191-204. Springer, 2017.","title":"Blending lazygrounding and CDNL search for answer-set solving","authors":"Antonius Weinzierl, Weinzierl","year":"2017","venue":"Proc. 14th Int. Conf. on Logic Programming and Nonmonotonic Reasoning (LPNMR'17)","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}