{"type":"ScholarlyArticle","title":"Explanations for Negative Query Answers under Inconsistency-Tolerant Semantics","authors":[{"name":"Thomas Lukasiewicz","slug":"thomas-lukasiewicz","given":"Thomas","family":"Lukasiewicz","affiliation":"Institute of Logic and Computation , TU Wien , Austria; Department of Computer Science , University of Oxford , UK"},{"name":"Enrico Malizia","slug":"enrico-malizia","given":"Enrico","family":"Malizia","affiliation":"DISI , University of Bologna , Italy"},{"name":"Cristian Molinaro","slug":"cristian-molinaro","given":"Cristian","family":"Molinaro","affiliation":"DIMES , University of Calabria , Italy"}],"abstract":"Inconsistency-tolerant semantics have been proposed to provide meaningful query answers even in the presence of inconsistent knowledge. Recently, explainability has also become a prominent problem in different areas of AI. While the complexity of inconsistency-tolerant semantics is rather well-understood, not much attention has been paid yet to the problem of explaining query answers when inconsistencies may exist. Recent work on existential rules in the inconsistent setting has focused only on understanding why a query is entailed.\r\nIn this paper, we address another important problem, which is explaining why a query is not entailed under an inconsistency-tolerant semantics. In particular, we consider three popular  semantics, namely, the ABox repair, the intersection of repairs, and the intersection of closed repairs. We provide a thorough complexity analysis for a wide range of existential rule languages and for several complexity measures.","doi":"10.24963/ijcai.2022/375","url":"https://ijcai.org/proceedings/2022/375","pdf":"https://ijcai.org/proceedings/2022/0375.pdf","markdown":"https://ijcai.org/proceedings/2022/375.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/375","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":375,"pages":{"first":2705,"last":2711},"keywords":["Knowledge Representation and Reasoning: Computational Complexity of Reasoning"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986915","length_sec":85,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985058","length_sec":360,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Arenas et al., 1999] Marcelo Arenas, Leopoldo E. Bertossi, and Jan Chomicki. Consistent query answers in inconsistent databases. In Proc. PODS, pages 68-79, 1999.","title":"Consistent query answers in inconsistent databases","authors":"Marcelo Arenas, Leopoldo E Bertossi, Jan Chomicki","year":"1999","venue":"Proc. PODS","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Arioua et al., 2015] Abdallah Arioua, Nouredine Tamani, and Madalina Croitoru. Query answering explanation in inconsistent Datalog+/-knowledge bases. In Proc. DEXA, pages 203-219, 2015.","title":"Query answering explanation in inconsistent Datalog+/-knowledge bases","authors":"Abdallah Arioua, Nouredine Tamani, Madalina Croitoru","year":"2015","venue":"Proc. DEXA","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bienvenu and Bourgaux, 2016] Meghyn Bienvenu and Ca- mille Bourgaux. Inconsistency-tolerant querying of de- scription logic knowledge bases. In Reasoning Web, pages 156-202, 2016.","title":"Meghyn Bienvenu and Camille Bourgaux. Inconsistency-tolerant querying of description logic knowledge bases","authors":"Bourgaux Bienvenu","year":"2016","venue":"Reasoning Web","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bienvenu and Rosati, 2013] Meghyn Bienvenu and Riccar- do Rosati. Tractable approximations of consistent query answering for robust ontology-based data access. In Proc. IJCAI, pages 775-781, 2013.","title":"Meghyn Bienvenu and Riccardo Rosati. Tractable approximations of consistent query answering for robust ontology-based data access","authors":"Rosati Bienvenu","year":"2013","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bienvenu et al., 2014] Meghyn Bienvenu, Camille Bour- gaux, and François Goasdoué. Querying inconsistent de- scription logic knowledge bases under preferred repair se- mantics. In Proc. AAAI, pages 996-1002, 2014.","title":"Querying inconsistent description logic knowledge bases under preferred repair semantics","authors":"Bienvenu","year":"2014","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bienvenu et al., 2015] Meghyn Bienvenu, Camille Bour- gaux, and François Goasdoué. Explaining query answers under inconsistency-tolerant semantics over description logic knowledge bases. In Proc. DL, 2015.","title":"Explaining query answers under inconsistency-tolerant semantics over description logic knowledge bases","authors":"Bienvenu","year":"2015","venue":"Proc. DL","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bienvenu et al., 2016] Meghyn Bienvenu, Camille Bour- gaux, and François Goasdoué. Explaining inconsistency- tolerant query answering over description logic knowledge bases. In Proc. AAAI, pages 900-906, 2016.","title":"Explaining inconsistencytolerant query answering over description logic knowledge bases","authors":"Bienvenu","year":"2016","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Bienvenu et al., 2019] Meghyn Bienvenu, Camille Bour- gaux, and François Goasdoué. Computing and explaining query answers over inconsistent DL-Lite knowledge bases. J. Artif. Intell. Res., 64:563-644, 2019.","title":"Computing and explaining query answers over inconsistent DL-Lite knowledge bases","authors":"Bienvenu","year":"2019","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Bienvenu, 2012] Meghyn Bienvenu. On the complexity of consistent query answering in the presence of simple on- tologies. In Proc. AAAI, pages 705-711, 2012.","title":"On the complexity of consistent query answering in the presence of simple ontologies","authors":"Meghyn Bienvenu, Bienvenu","year":"2012","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Calì et al., 2012a] Andrea Calì, Georg Gottlob, and Thomas Lukasiewicz. A general Datalog-based framework for tractable query answering over ontologies. J. Web Sem., 14:57-83, 2012.","title":"A general Datalog-based framework for tractable query answering over ontologies","authors":"Calì","year":"2012","venue":"J. Web Sem","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Calì et al., 2012b] Andrea Calì, Georg Gottlob, and Andreas Pieris. Towards more expressive ontology languages: The query answering problem. Artif. Intell., 193:87-128, 2012.","title":"Towards more expressive ontology languages: The query answering problem","authors":"Calì","year":"2012","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Calì et al., 2013] Andrea Calì, Georg Gottlob, and Michael Kifer. Taming the infinite chase: Query answering un- der expressive relational constraints. J. Artif. Intell. Res., 48:115-174, 2013.","title":"Taming the infinite chase: Query answering under expressive relational constraints","authors":"Andrea Calì, Georg Gottlob, Michael Kifer","year":"2013","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Ceylan et al., 2019] İsmail İlkan Ceylan, Thomas Lukasie- wicz, Enrico Malizia, and Andrius Vaicenavičius. Expla- nations for query answers under existential rules. In Proc. IJCAI, pages 1639-1646, 2019.","title":"Explanations for query answers under existential rules","authors":"Thomas İsmail İlkan Ceylan, Enrico Lukasiewicz, Andrius Malizia, Vaicenavičius","year":"2019","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2019/227"},{"position":14,"raw":"[Ceylan et al., 2020a] İsmail İlkan Ceylan, Thomas Lukasi- ewicz, Enrico Malizia, Cristian Molinaro, and Andrius Vaicenavicius. Explanations for negative query answers under existential rules. In Proc. KR, pages 223-232, 2020.","title":"Explanations for negative query answers under existential rules","authors":"Ceylan","year":"2020","venue":"Proc. KR","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Ceylan et al., 2020b] İsmail İlkan Ceylan, Thomas Lukasie- wicz, Enrico Malizia, and Andrius Vaicenavicius. Explana- tions for ontology-mediated query answering in description logics. In Proc. ECAI, pages 672-679, 2020.","title":"Explanations for ontology-mediated query answering in description logics","authors":"Ceylan","year":"2020","venue":"Proc. ECAI","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Ceylan et al., 2021] İsmail İlkan Ceylan, Thomas Lukasi- ewicz, Enrico Malizia, Cristian Molinaro, and Andrius Vaicenavicius. Preferred explanations for ontology-media- ted queries under existential rules. In Proc. AAAI, pages 6262-6270, 2021.","title":"Preferred explanations for ontology-mediated queries under existential rules","authors":"Thomas İsmail İlkan Ceylan, Enrico Lukasiewicz, Cristian Malizia, Andrius Molinaro, Vaicenavicius","year":"2021","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Eiter et al., 2016] Thomas Eiter, Thomas Lukasiewicz, and Livia Predoiu. Generalized consistent query answering under existential rules. In Proc. KR, pages 359-368, 2016.","title":"Generalized consistent query answering under existential rules","authors":"Thomas Eiter, Thomas Lukasiewicz, Livia Predoiu","year":"2016","venue":"Proc. KR","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Fagin et al., 2005] Ronald Fagin, Phokion G. Kolaitis, Re- née J. Miller, and Lucian Popa. Data exchange: semantics and query answering. Theor. Comput. Sci., 336(1):89-124, 2005.","title":"Data exchange: semantics and query answering","authors":"Ronald Fagin, G Phokion, Renée J Kolaitis, Lucian Miller, Popa","year":"2005","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Gottlob and Malizia, 2018] Georg Gottlob and Enrico Mali- zia. Achieving new upper bounds for the hypergraph duality problem through logic. SIAM J. Comput., 47(2):456-492, 2018.","title":"Achieving new upper bounds for the hypergraph duality problem through logic","authors":"Malizia Gottlob","year":"2018","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Hecham et al., 2017] Abdelraouf Hecham, Abdallah Arioua, Gem Stapleton, and Madalina Croitoru. An empirical evalu- ation of argumentation in explaining inconsistency-tolerant query answering. In Proc. DL, 2017.","title":"Abdelraouf Hecham, Abdallah Arioua, Gem Stapleton, and Madalina Croitoru. An empirical evaluation of argumentation in explaining inconsistency-tolerant query answering","authors":"Hecham","year":"2017","venue":"Proc. DL","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Hemachandra, 1989] Lane A. Hemachandra. The strong exponential hierarchy collapses. J. Comput. Syst. Sci., 39(3):299-322, 1989.","title":"The strong exponential hierarchy collapses","authors":"Lane A Hemachandra","year":"1989","venue":"J. Comput. Syst. Sci","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Lembo et al., 2010] Domenico Lembo, Maurizio Lenzerini, Riccardo Rosati, Marco Ruzzi, and Domenico Fabio Savo. Inconsistency-tolerant semantics for description logics. In Proc. RR, pages 103-117, 2010.","title":"Inconsistency-tolerant semantics for description logics","authors":"Domenico Lembo, Maurizio Lenzerini, Riccardo Rosati, Marco Ruzzi, Domenico Fabio Savo","year":"2010","venue":"Proc. RR","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Lembo et al., 2015] Domenico Lembo, Maurizio Lenzerini, Riccardo Rosati, Marco Ruzzi, and Domenico Fabio Savo. Inconsistency-tolerant query answering in ontology-based data access. J. Web Sem., 33:3-29, 2015.","title":"Inconsistency-tolerant query answering in ontology-based data access","authors":"Domenico Lembo, Maurizio Lenzerini, Riccardo Rosati, Marco Ruzzi, Domenico Fabio Savo","year":"2015","venue":"J. Web Sem","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Lukasiewicz and Malizia, 2017] Thomas Lukasiewicz and Enrico Malizia. A novel characterization of the complex- ity class Θ P k based on counting and comparison. Theor. Comput. Sci., 694:21-33, 2017.","title":"A novel characterization of the complexity class Θ P k based on counting and comparison","authors":"Thomas Lukasiewicz, Enrico Malizia","year":"2017","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Lukasiewicz et al., 2018] Thomas Lukasiewicz, Enrico Ma- lizia, and Cristian Molinaro. Complexity of approximate query answering under inconsistency in Datalog+/-. In Proc. IJCAI, pages 1921-1927, 2018.","title":"Complexity of approximate query answering under inconsistency in Datalog+","authors":"Thomas Lukasiewicz, Enrico Malizia, Cristian Molinaro","year":"2018","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2018/265"},{"position":26,"raw":"[Lukasiewicz et al., 2019] Thomas Lukasiewicz, Enrico Ma- lizia, and Andrius Vaicenavičius. Complexity of incon- sistency-tolerant query answering in Datalog+/-under cardinality-based repairs. In Proc. AAAI, pages 2962-2969, 2019.","title":"Complexity of inconsistency-tolerant query answering in Datalog+/-under cardinality-based repairs","authors":"Thomas Lukasiewicz, Enrico Malizia, Andrius Vaicenavičius","year":"2019","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Lukasiewicz et al., 2020] Thomas Lukasiewicz, Enrico Ma- lizia, and Cristian Molinaro. Explanations for inconsist- ency-tolerant query answering under existential rules. In Proc. AAAI, pages 2909-2916, 2020.","title":"Explanations for inconsistency-tolerant query answering under existential rules","authors":"Thomas Lukasiewicz, Enrico Malizia, Cristian Molinaro","year":"2020","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Lukasiewicz et al., 2022] Thomas Lukasiewicz, Enrico Ma- lizia, Maria Vanina Martinez, Cristian Molinaro, Andreas Pieris, and Gerardo I. Simari. Inconsistency-tolerant query answering for existential rules. Artif. Intell., 307:103685, 2022.","title":"Inconsistency-tolerant query answering for existential rules","authors":"Thomas Lukasiewicz, Enrico Malizia, Maria Vanina Martinez, Cristian Molinaro, Andreas Pieris, Gerardo I Simari","year":"2022","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Tsamoura et al., 2021] Efthymia Tsamoura, David Carral, Enrico Malizia, and Jacopo Urbani. Materializing knowl- edge bases via trigger graphs. Proc. VLDB Endow., 14(6):943-956, 2021.","title":"Materializing knowledge bases via trigger graphs","authors":"Tsamoura","year":"2021","venue":"Proc. VLDB Endow","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Vardi, 1982] Moshe Y. Vardi. The complexity of relational query languages. In Proc. STOC, pages 137-146, 1982.","title":"The complexity of relational query languages","authors":"Moshe Y Vardi","year":"1982","venue":"Proc. STOC","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}