{"type":"ScholarlyArticle","title":"Learning Description Logic Concepts: When can Positive and Negative Examples be Separated?","authors":[{"name":"Maurice Funk","slug":"maurice-funk","given":"Maurice","family":"Funk","affiliation":"Department of Computer Science , University of Bremen"},{"name":"Jean Christoph Jung","slug":"jean-christoph-jung","given":"Jean Christoph","family":"Jung","affiliation":"Department of Computer Science , University of Bremen"},{"name":"Carsten Lutz","slug":"carsten-lutz","given":"Carsten","family":"Lutz","affiliation":"Department of Computer Science , University of Bremen"},{"name":"Hadrien Pulcini","slug":"hadrien-pulcini","given":"Hadrien","family":"Pulcini","affiliation":"Department of Computer Science , University of Liverpool"},{"name":"Frank Wolter","slug":"frank-wolter","given":"Frank","family":"Wolter","affiliation":"Department of Computer Science , University of Liverpool"}],"abstract":"Learning description logic (DL) concepts from positive and negative examples given in the form of labeled data items in a KB has received significant attention in the literature. We study the fundamental question of when a separating DL concept exists and provide useful model-theoretic characterizations as well as complexity results for the associated decision problem. For expressive DLs such as ALC and ALCQI, our characterizations show a surprising link to the evaluation of ontology-mediated conjunctive queries. We exploit this to determine the combined complexity (between ExpTime and NExpTime) and data complexity (second level of the polynomial hierarchy) of separability. For the Horn DL EL, separability is ExpTime-complete both in combined and in data complexity while for its modest extension ELI it is even undecidable.  Separability is also undecidable when the KB is formulated in ALC and the separating concept is required to be in EL or ELI.","doi":"10.24963/ijcai.2019/233","url":"https://ijcai.org/proceedings/2019/233","pdf":"https://ijcai.org/proceedings/2019/0233.pdf","markdown":"https://ijcai.org/proceedings/2019/233.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/233","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":233,"pages":{"first":1682,"last":1688},"keywords":["Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Description Logics and Ontologies"],"videos":[],"references":[{"position":1,"raw":"[Baader et al., 2017] Franz Baader, Ian Horrocks, Carsten Lutz, and Ulrike Sattler. An Introduction to Description Logic. Cambridge University Press, 2017.","title":"An Introduction to Description Logic","authors":"Baader","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Baader, 2003] Franz Baader. Least common subsumers and most specific concepts in a description logic with existen- tial restrictions and terminological cycles. In Proc. of IJ- CAI, pages 319-324, 2003.","title":"Least common subsumers and most specific concepts in a description logic with existential restrictions and terminological cycles","authors":"Franz Baader, Baader","year":"2003","venue":"Proc. of IJ-CAI","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Badea and Nienhuys-Cheng, 2000] Liviu Badea and Shan- Hwei Nienhuys-Cheng. A refinement operator for descrip- tion logics. In Proc. of ILP, pages 40-59, 2000.","title":"A refinement operator for description logics","authors":"Nienhuys-Cheng ; Badea, Liviu Badea, Shan-Hwei Nienhuys-Cheng","year":"2000","venue":"Proc. of ILP","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bienvenu et al., 2014] Meghyn Bienvenu, Balder ten Cate, Carsten Lutz, and Frank Wolter. Ontology-based data ac- cess: A study through disjunctive datalog, CSP, and MM- SNP. ACM Trans. Database Syst., 39(4):33:1-33:44, 2014.","title":"Ontology-based data access: A study through disjunctive datalog, CSP, and MM-SNP","authors":"Bienvenu","year":"2014","venue":"ACM Trans. Database Syst","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Botoeva et al., 2019] Elena Botoeva, Roman Kontchakov, Carsten Lutz, Vladislav Ryzhikov, Frank Wolter, and Michael Zakharyaschev. Query inseparability for ALC on- tologies. Artif. Intell., 272:1-51, 2019.","title":"Query inseparability for ALC ontologies","authors":"Elena Botoeva, Roman Kontchakov, Carsten Lutz, Vladislav Ryzhikov, Frank Wolter, Michael Zakharyaschev","year":"2019","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bühmann et al., 2016] Lorenz Bühmann, Jens Lehmann, and Patrick Westphal. DL-learner -A framework for in- ductive 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":7,"raw":"[Bühmann et al., 2018] Lorenz Bühmann, Jens Lehmann, Patrick Westphal, and Simon Bin. DL-learner structured machine learning on semantic web data. In Proc. of WWW, pages 467-471, 2018.","title":"DL-learner structured machine learning on semantic web data","authors":"Jens Lorenz Bühmann, Patrick Lehmann, Simon Westphal, Bin","year":"2018","venue":"Proc. of WWW","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Calvanese et al., 2013] Diego Calvanese, Giuseppe De Gi- acomo, Domenico Lembo, Maurizio Lenzerini, and Ric- cardo Rosati. Data complexity of query answering in de- scription logics. Artif. Intell., 195:335-360, 2013.","title":"Data complexity of query answering in description logics","authors":"Calvanese","year":"2013","venue":"Artif. Intell","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 ex- pression 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":"[Goranko and Otto, 2007] Valentin Goranko and Martin Otto. Model theory of modal logic. In Handbook of Modal Logic, pages 249-329. Elsevier, 2007.","title":"Model theory of modal logic","authors":"Valentin Goranko, Martin Otto","year":"2007","venue":"Handbook of Modal Logic","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Gutiérrez-Basulto et al., 2018] Víctor Gutiérrez-Basulto, Jean Christoph Jung, and Leif Sabellek. Reverse engi- neering queries in ontology-enriched systems: The case of expressive horn description logic ontologies. In Proc. of IJCAI-ECAI, 2018.","title":"Reverse engineering queries in ontology-enriched systems: The case of expressive horn description logic ontologies","authors":"Gutiérrez-Basulto","year":"2018","venue":"Proc. of IJCAI-ECAI","doi":null,"url":null,"internal_url":"/proceedings/2018/255"},{"position":12,"raw":"[Harel et al., 2002] David Harel, Orna Kupferman, and Moshe Y. Vardi. On the complexity of verifying con- current transition systems. Inf. Comput., 173(2):143-161, 2002.","title":"On the complexity of verifying concurrent transition systems","authors":"David Harel, Orna Kupferman, Moshe Y Vardi","year":"2002","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hirsh et al., 2004] Haym Hirsh, Nina Mishra, and Leonard Pitt. Version spaces and the consistency problem. Artif. Intell., 156(2):115-138, 2004.","title":"Version spaces and the consistency problem","authors":"Haym Hirsh, Nina Mishra, Leonard Pitt","year":"2004","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Iannone et al., 2007] Luigi Iannone, Ignazio Palmisano, and Nicola Fanizzi. An algorithm based on counterfactu- als 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":15,"raw":"[Kietz, 1993] Jörg-Uwe Kietz. Some lower bounds for the computational complexity of inductive logic program- ming. In Proc. of ECML, pages 115-123, 1993.","title":"Some lower bounds for the computational complexity of inductive logic programming","authors":"Jörg-Uwe Kietz, Kietz","year":"1993","venue":"Proc. of ECML","doi":null,"url":null,"internal_url":null},{"position":16,"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":17,"raw":"[Lehmann and Hitzler, 2010] Jens Lehmann and Pascal Hit- zler. Concept learning in description logics using refine- ment operators. Machine Learning, 78:203-250, 2010.","title":"Concept learning in description logics using refinement operators","authors":"Hitzler Lehmann, Jens Lehmann, Pascal Hitzler","year":"2010","venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Lehmann and Völker, 2014] Jens Lehmann and Johanna Völker. Perspectives on Ontology Learning, volume 18 of Studies on the Semantic Web. IOS Press, 2014.","title":"Perspectives on Ontology Learning","authors":"Völker Lehmann","year":"2014","venue":"Studies on the Semantic Web","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lehmann et al., 2014] Jens Lehmann, Nicola Fanizzi, Lorenz Bühmann, and Claudia d'Amato. Concept learn- ing. In Perspectives on Ontology Learning, pages 71-91. AKA / IOS Press, 2014.","title":"Concept learning","authors":"Lehmann","year":"2014","venue":"Perspectives on Ontology Learning","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Lisi, 2012] Francesca A. Lisi. A formal characterization of concept learning in description logics. In Proc. of DL, 2012.","title":"A formal characterization of concept learning in description logics","authors":"Francesca A Lisi","year":"2012","venue":"Proc. of DL","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Lutz et al., 2010] Carsten Lutz, Robert Piro, and Frank Wolter. Enriching EL-concepts with greatest fixpoints. In Proc. of ECAI, pages 41-46, 2010.","title":"Enriching EL-concepts with greatest fixpoints","authors":"Carsten Lutz, Robert Piro, Frank Wolter","year":"2010","venue":"Proc. of ECAI","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Lutz et al., 2011] Carsten Lutz, Robert Piro, and Frank Wolter. Description logic TBoxes: Model-theoretic char- acterizations and rewritability. In Proc. of IJCAI, 2011.","title":"Description logic TBoxes: Model-theoretic characterizations and rewritability","authors":"Carsten Lutz, Robert Piro, Frank Wolter","year":"2011","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Lutz, 2008] Carsten Lutz. The complexity of conjunctive query answering in expressive description logics. In Proc. of IJCAR, pages 179-193, 2008.","title":"The complexity of conjunctive query answering in expressive description logics","authors":"Carsten Lutz","year":"2008","venue":"Proc. of IJCAR","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Pitt and Valiant, 1988] Leonard Pitt and Leslie G. Valiant. Computational limitations on learning from examples. J. ACM, 35(4):965-984, 1988.","title":"Computational limitations on learning from examples","authors":"Leonard Pitt, Leslie G Valiant","year":"1988","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Rutenburg, 1986] Vladislav Rutenburg. Complexity of gen- eralized graph coloring. In Proc. of MFCS, pages 573- 581, 1986.","title":"Complexity of generalized graph coloring","authors":"Vladislav Rutenburg","year":"1986","venue":"Proc. of MFCS","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Sarker et al., 2017] Md. Kamruzzaman Sarker, Ning Xie, Derek Doran, Michael Raymer, and Pascal Hitzler. Ex- plaining trained neural networks with semantic web tech- nologies: First steps. In Proc. of NeSy, 2017.","title":"Explaining trained neural networks with semantic web technologies: First steps","authors":"Kamruzzaman Md, Ning Sarker, Derek Xie, Michael Doran, Pascal Raymer, Hitzler","year":"2017","venue":"Proc. of NeSy","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Straccia and Mucci, 2015] Umberto Straccia and Matteo Mucci. pFOIL-DL: Learning (fuzzy) EL concept descrip- tions from crisp OWL data using a probabilistic ensemble estimation. In Proc. of SAC, pages 345-352. ACM, 2015.","title":"Umberto Straccia and Matteo Mucci. pFOIL-DL: Learning (fuzzy) EL concept descriptions from crisp OWL data using a probabilistic ensemble estimation","authors":"Mucci Straccia","year":"2015","venue":"Proc. of SAC","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Tran et al., 2014] Thanh-Luong Tran, Quang-Thuy Ha, Thi-Lan-Giao Hoang, Linh Anh Nguyen, and Hung Son Nguyen. Bisimulation-based concept learning in descrip- tion logics. Fundam. Inform., 133(2-3):287-303, 2014.","title":"Bisimulation-based concept learning in description logics","authors":"Thanh-Luong Tran, Quang-Thuy Ha, Thi-Lan-Giao Hoang, Linh Anh Nguyen, Hung Son Nguyen","year":"2014","venue":"Fundam. Inform","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Zarrieß and Turhan, 2013] Benjamin Zarrieß and Anni- Yasmin Turhan. Most specific generalizations w.r.t. gen- eral 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":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}