{"type":"ScholarlyArticle","title":"SAT-Based PAC Learning of Description Logic Concepts","authors":[{"name":"Balder ten Cate","slug":"balder-ten-cate","given":"Balder","family":"ten Cate","affiliation":"ILLC , University of Amsterdam"},{"name":"Maurice Funk","slug":"maurice-funk","given":"Maurice","family":"Funk","affiliation":"Leipzig University; Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI)"},{"name":"Jean Christoph Jung","slug":"jean-christoph-jung","given":"Jean Christoph","family":"Jung","affiliation":"TU Dortmund University"},{"name":"Carsten Lutz","slug":"carsten-lutz","given":"Carsten","family":"Lutz","affiliation":"Leipzig University; Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI)"}],"abstract":"We propose bounded fitting as a scheme for learning\r\ndescription logic concepts in the presence of ontologies. A main\r\nadvantage is that the resulting learning algorithms come with\r\ntheoretical guarantees regarding their generalization to unseen\r\nexamples in the sense of PAC learning. We prove that, in contrast,\r\nseveral other natural learning algorithms fail to provide such\r\nguarantees. As a further contribution, we present the system SPELL\r\nwhich efficiently implements bounded fitting for the description\r\nlogic ELHr based on a SAT solver, and compare its performance to a\r\nstate-of-the-art learner.","doi":"10.24963/ijcai.2023/373","url":"https://ijcai.org/proceedings/2023/373","pdf":"https://ijcai.org/proceedings/2023/0373.pdf","markdown":"https://ijcai.org/proceedings/2023/373.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/373","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":373,"pages":{"first":3347,"last":3355},"keywords":["Knowledge Representation and Reasoning: KRR: Learning and reasoning","Knowledge Representation and Reasoning: KRR: Description logics and ontologies"],"videos":[],"references":[{"position":1,"raw":"[Angluin, 1987] Dana Angluin. Queries and concept learning. Mach. Learn., 2(4):319-342, 1987.","title":"Dana Angluin. Queries and concept learning","authors":"Angluin","year":"1987","venue":"Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Baader et al., 2008] Franz Baader, Carsten Lutz, and Sebas- tian Brandt. Pushing the EL envelope further. In Proc. of OWLED. CEUR-WS.org, 2008.","title":"Pushing the EL envelope further","authors":"Franz Baader, Carsten Lutz, Sebastian Brandt","year":"2008","venue":"Proc. of OWLED. CEUR-WS.org","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Baader et al., 2017] Franz Baader, Ian Horrocks, Carsten Lutz, and Ulrike Sattler. An Introduction to Description Logics. Cambridge University Press, 2017.","title":"An Introduction to Description Logics","authors":"Baader","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Biere et al., 1999] Armin Biere, Alessandro Cimatti, Ed- mund M. Clarke, and Yunshan Zhu. Symbolic model check- ing without BDDs. In Proc. of TACAS, pages 193-207. Springer, 1999.","title":"Symbolic model checking without BDDs","authors":"Armin Biere, Alessandro Cimatti, Edmund M Clarke, Yunshan Zhu","year":"1999","venue":"Proc. of TACAS","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Blumer et al., 1989] Anselm Blumer, Andrzej Ehrenfeucht, David Haussler, and Manfred K. Warmuth. Learnability and the Vapnik-Chervonenkis dimension. J. ACM, 36(4):929- 965, 1989.","title":"Learnability and the Vapnik-Chervonenkis dimension","authors":"Anselm Blumer, Andrzej Ehrenfeucht, David Haussler, Manfred K Warmuth","year":"1989","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"Raymond A. Board and Leonard Pitt. On the necessity of Occam algorithms. Theor. Comput. Sci., 100(1):157-184, 1992.","title":"On the necessity of Occam algorithms","authors":"Raymond A Board, Leonard Pitt","year":"1992","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bühmann et al., 2016] Lorenz Bühmann, Jens Lehmann, and Patrick Westphal. DL-Learner -A framework for induc- tive learning on the semantic web. J. Web Sem., 39:15-24, 2016.","title":"DL-Learner -A framework for inductive learning on the semantic web","authors":"Jens Lorenz Bühmann, Patrick Lehmann, Westphal","year":"2016","venue":"J. Web Sem","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Cohen and Hirsh, 1994] William W. Cohen and Haym Hirsh. The learnability of description logics with equality con- straints. Mach. Learn., 17(2-3):169-199, 1994.","title":"The learnability of description logics with equality constraints","authors":"William W Cohen, Haym Hirsh","year":"1994","venue":"Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Fanizzi et al., 2018] Nicola Fanizzi, Giuseppe Rizzo, Clau- dia d'Amato, and Floriana Esposito. DLFoil: Class expres- sion learning revisited. In Proc. of EKAW, pages 98-113, 2018.","title":"DLFoil: Class expression learning revisited","authors":"Nicola Fanizzi, Giuseppe Rizzo, Claudia Amato, Floriana Esposito","year":"2018","venue":"Proc. of EKAW","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Frazier and Pitt, 1996] Michael Frazier and Leonard Pitt. Classic learning. Mach. Learn., 25(2-3):151-193, 1996.","title":"Classic learning","authors":"Michael Frazier, Leonard Pitt","year":"1996","venue":"Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Funk et al., 2019] Maurice Funk, Jean Christoph Jung, Carsten Lutz, Hadrien Pulcini, and Frank Wolter. Learning description logic concepts: When can positive and neg- ative examples be separated? In Proc. of IJCAI, pages 1682-1688, 2019.","title":"Learning description logic concepts: When can positive and negative examples be separated?","authors":"Maurice Funk, Jean, Christoph Jung, Carsten Lutz, Hadrien Pulcini, Frank Wolter","year":"2019","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2019/233"},{"position":12,"raw":"[Funk et al., 2021] Maurice Funk, Jean Christoph Jung, and Carsten Lutz. Actively learning concept and conjunctive queries under EL r -ontologies. In Proc. of IJCAI, pages 1887-1893, 2021.","title":"Actively learning concept and conjunctive queries under EL r -ontologies","authors":"Maurice Funk, Jean, Christoph Jung, Carsten Lutz","year":"2021","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Funk et al., 2022a] Maurice Funk, Jean Christoph Jung, and Carsten Lutz. Exact learning of ELI queries in the pres- ence of DL-Lite-Horn ontologies. In Proc. of DL. CEUR- WS.org, 2022.","title":"Exact learning of ELI queries in the presence of DL-Lite-Horn ontologies","authors":"Funk","year":"2022","venue":"Proc. of DL. CEUR-WS.org","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Funk et al., 2022b] Maurice Funk, Jean Christoph Jung, and Carsten Lutz. Frontiers and exact learning of ELI queries under DL-Lite ontologies. In Proc. of IJCAI, 2022.","title":"Frontiers and exact learning of ELI queries under DL-Lite ontologies","authors":"Funk","year":"2022","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2022/364"},{"position":15,"raw":"[Funk, 2019] Maurice Funk. Concept-by-Example in EL Knowledge Bases. Master's thesis, University of Bremen, 2019.","title":"Concept-by-Example in EL Knowledge Bases","authors":"Maurice Funk","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Gottlob et al., 1999] Georg Gottlob, Nicola Leone, and Francesco Scarcello. On the complexity of some induc- tive logic programming problems. New Gener. Comput., 17(1):53-75, 1999.","title":"On the complexity of some inductive logic programming problems","authors":"Gottlob","year":"1999","venue":"New Gener. Comput","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Iannone et al., 2007] Luigi Iannone, Ignazio Palmisano, and Nicola Fanizzi. An algorithm based on counterfactuals for concept learning in the semantic web. Appl. Intell., 26(2):139-159, 2007.","title":"An algorithm based on counterfactuals for concept learning in the semantic web","authors":"Luigi Iannone, Ignazio Palmisano, Nicola Fanizzi","year":"2007","venue":"Appl. Intell","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Jung et al., 2020] Jean Christoph Jung, Carsten Lutz, and Frank Wolter. Least general generalizations in description logic: Verification and existence. In Proc. of AAAI, pages 2854-2861. AAAI Press, 2020.","title":"Least general generalizations in description logic: Verification and existence","authors":"Jung","year":"2020","venue":"Proc. of AAAI","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Jung et al., 2021] Jean Christoph Jung, Carsten Lutz, Hadrien Pulcini, and Frank Wolter. Separating data exam- ples by description logic concepts with restricted signatures. In Proc. of KR, pages 390-399, 2021.","title":"Separating data examples by description logic concepts with restricted signatures","authors":"Jung","year":"2021","venue":"Proc. of KR","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Kietz, 1993] Jörg-Uwe Kietz. Some lower bounds for the computational complexity of inductive logic programming. In Proc. of ECML, pages 115-123, 1993.","title":"Some lower bounds for the computational complexity of inductive logic programming","authors":"Jörg-Uwe Kietz","year":"1993","venue":"Proc. of ECML","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Kriegel, 2019] Francesco Kriegel. Constructing and Extend- ing Description Logic Ontologies using Methods of Formal Concept Analysis. PhD thesis, TU Dresden, 2019.","title":"Constructing and Extending Description Logic Ontologies using Methods of Formal Concept Analysis","authors":"Francesco Kriegel","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Kriegel, 2021] Francesco Kriegel. Navigating the EL sub- sumption hierarchy. In Proc. of DL. CEUR-WS.org, 2021.","title":"Navigating the EL subsumption hierarchy","authors":"Francesco Kriegel","year":"2021","venue":"Proc. of DL. CEUR-WS.org","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Lehmann and Haase, 2009] Jens Lehmann and Christoph Haase. Ideal downward refinement in the EL description logic. In Proc. of ILP, pages 73-87, 2009.","title":"Ideal downward refinement in the EL description logic","authors":"Haase Lehmann, Jens Lehmann, Christoph Haase","year":"2009","venue":"Proc. of ILP","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Lehmann and Hitzler, 2010] Jens Lehmann and Pascal Hit- zler. Concept learning in description logics using refine- ment operators. Mach. Learn., 78:203-250, 2010.","title":"Concept learning in description logics using refinement operators","authors":"Hitzler Lehmann","year":"2010","venue":"Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Lutz et al., 2009] Carsten Lutz, David Toman, and Frank Wolter. Conjunctive query answering in the description logic EL using a relational database system. In Proc. of IJCAI, pages 2070-2075, 2009.","title":"Conjunctive query answering in the description logic EL using a relational database system","authors":"Carsten Lutz, David Toman, Frank Wolter","year":"2009","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2009/341"},{"position":26,"raw":"[Nesetril and Tardif, 2000] Jaroslav Nesetril and Claude Tardif. Duality theorems for finite structures (character- ising gaps and good characterisations). J. Comb. Theory, Ser. B, 80(1):80-97, 2000.","title":"Jaroslav Nesetril and Claude Tardif. Duality theorems for finite structures (characterising gaps and good characterisations)","authors":"Tardif Nesetril","year":"2000","venue":"J. Comb. Theory, Ser. B","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Nesetril and Tardif, 2005] Jaroslav Nesetril and Claude Tardif. Short answers to exponentially long questions: Ex- tremal aspects of homomorphism duality. SIAM J. Discret. Math., 19(4):914-920, 2005.","title":"Short answers to exponentially long questions: Extremal aspects of homomorphism duality","authors":"Tardif Nesetril, Jaroslav Nesetril, Claude Tardif","year":"2005","venue":"SIAM J. Discret. Math","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Singh et al., 2020] Gunjan Singh, Sumit Bhatia, and Raghava Mutharaju. OWL2Bench: A benchmark for OWL 2 reasoners. In Proc. of ISWC, pages 81-96. Springer, 2020.","title":"OWL2Bench: A benchmark for OWL 2 reasoners","authors":"Gunjan Singh, Sumit Bhatia, Raghava Mutharaju","year":"2020","venue":"Proc. of ISWC","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Tanon et al., 2020] Thomas Pellissier Tanon, Gerhard Weikum, and Fabian M. Suchanek. YAGO 4: A reason- able knowledge base. In Proc. of ESWC, pages 583-596. Springer, 2020.","title":"YAGO 4: A reasonable knowledge base","authors":"Thomas Pellissier Tanon, Gerhard Weikum, Fabian M Suchanek","year":"2020","venue":"Proc. of ESWC","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[ten Cate and Dalmau, 2021] Balder ten Cate and Victor Dal- mau. Conjunctive queries: Unique characterizations and exact learnability. In Proc. of ICDT, volume 186 of LIPIcs, pages 9:1-9:24. Schloss Dagstuhl -Leibniz-Zentrum für Informatik, 2021.","title":"Balder ten Cate and Victor Dalmau. Conjunctive queries: Unique characterizations and exact learnability","authors":"Dalmau Cate","year":"2021","venue":"Proc. of ICDT","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[ten Cate et al., 2022] Balder ten Cate, Maurice Funk, Jean Christoph Jung, and Carsten Lutz. On the non-efficient PAC learnability of acyclic conjunctive queries. CoRR, abs/2208.10255, 2022.","title":"On the non-efficient PAC learnability of acyclic conjunctive queries","authors":"Cate Ten","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[ten Cate et al., 2023a] Balder ten Cate, Victor Dalmau, Mau- rice Funk, and Carsten Lutz. Extremal fitting problems for conjunctive queries. In Proc. of PODS, 2023.","title":"Extremal fitting problems for conjunctive queries","authors":"Cate Ten","year":"2023","venue":"Proc. of PODS","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[ten Cate et al., 2023b] Balder ten Cate, Maurice Funk, Jean Christoph Jung, and Carsten Lutz. SAT-based PAC learning of description logic concepts. CoRR, abs/2305.08511, 2023.","title":"SAT-based PAC learning of description logic concepts","authors":"Cate Ten","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Valiant, 1984] Leslie G. Valiant. A theory of the learnable. Commun. ACM, 27(11):1134-1142, 1984.","title":"A theory of the learnable","authors":"Leslie G Valiant","year":"1984","venue":"Commun. ACM","doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Westphal et al., 2019] Patrick Westphal, Lorenz Bühmann, Simon Bin, Hajira Jabeen, and Jens Lehmann. SML-bench -A benchmarking framework for structured machine learn- ing. Semantic Web, 10(2):231-245, 2019.","title":"SML-bench -A benchmarking framework for structured machine learning","authors":"Patrick Westphal, Lorenz Bühmann, Simon Bin, Hajira Jabeen, Jens Lehmann","year":"2019","venue":"Semantic Web","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Zarrieß and Turhan, 2013] Benjamin Zarrieß and Anni- Yasmin Turhan. Most specific generalizations w.r.t. general EL-TBoxes. In Proc. of IJCAI, pages 1191-1197, 2013.","title":"Most specific generalizations w.r.t. general EL-TBoxes","authors":"Turhan Zarrieß, Benjamin Zarrieß, Anni-Yasmin Turhan","year":"2013","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2013/179"},{"position":37,"raw":"[Zhou et al., 2013] Yujiao Zhou, Bernardo Cuenca Grau, Ian Horrocks, Zhe Wu, and Jay Banerjee. Making the most of your triple store: query answering in OWL 2 using an RL reasoner. In WWW, pages 1569-1580. ACM, 2013.","title":"Making the most of your triple store: query answering in OWL 2 using an RL reasoner","authors":"Yujiao Zhou, Bernardo Cuenca Grau, Ian Horrocks, Zhe Wu, Jay Banerjee","year":"2013","venue":"WWW","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}