{"type":"ScholarlyArticle","title":"Explainable Certain Answers","authors":[{"name":"Giovanni Amendola","slug":"giovanni-amendola","given":"Giovanni","family":"Amendola","affiliation":"Mathematics and Computer Science , University of Calabria"},{"name":"Leonid Libkin","slug":"leonid-libkin","given":"Leonid","family":"Libkin","affiliation":"School of Informatics , University of Edinburgh"}],"abstract":"When a dataset is not fully specified and can represent many possible worlds, one commonly answers queries by computing certain answers to them.  A natural way of defining certainty is to say that an answer is certain if it is consistent with query answers in all possible worlds, and is furthermore the most informative answer with this property. However, the existence and complexity of such answers is not yet well understood even for relational databases. Thus in applications one tends to use different notions, essentially  the intersection of query answers in possible worlds. However, justification of such notions has long been questioned.  This leads to two problems: are certain answers based on informativeness feasible in applications? and can a clean justification be provided for intersection-based notions?\r\n\r\nOur goal is to answer both. For the former, we show that such answers may not exist, or be very large, even in simple cases of querying\r\nincomplete data. For the latter, we add the concept of explanations to the notion of informativeness: it shows not only that one object is more informative than the other, but also says why this is so.  This leads to a modified notion of certainty: explainable certain answers. We present a general framework for reasoning about them, and show that for open and closed world relational databases, they are precisely the common intersection-based notions of certainty.","doi":"10.24963/ijcai.2018/233","url":"https://ijcai.org/proceedings/2018/233","pdf":"https://ijcai.org/proceedings/2018/0233.pdf","markdown":"https://ijcai.org/proceedings/2018/233.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/233","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":233,"pages":{"first":1683,"last":1690},"keywords":["Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Logics for Knowledge Representation","Multidisciplinary Topics and Applications: Databases","Knowledge Representation and Reasoning: Knowledge Representation Languages"],"videos":[],"references":[{"position":1,"raw":"[Abiteboul et al., 1995] Serge Abiteboul, Richard Hull, and Victor Vianu. Foundations of Databases. Addison-Wesley, 1995.","title":"Foundations of Databases","authors":"Serge Abiteboul, Richard Hull, Victor Vianu","year":"1995","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Ahmetaj et al., 2015] Shqiponja Ahmetaj, Wolfgang Fischl, Reinhard Pichler, Mantas Simkus, and Sebastian Skritek. Towards reconciling SPARQL and certain answers. In WWW, pages 23-33, 2015.","title":"Towards reconciling SPARQL and certain answers","authors":"Ahmetaj","year":"2015","venue":"WWW","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Arenas et al., 2014] Marcelo Arenas, Pablo Barceló, Leonid Libkin, and Filip Murlak. Foundations of Data Exchange. Cambridge University Press, 2014.","title":"Foundations of Data Exchange","authors":"Marcelo Arenas, Pablo Barceló, Leonid Libkin, Filip Murlak","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Arenas et al., 2017] Marcelo Arenas, Elena Botoeva, Egor V. Kostylev, and Vladislav Ryzhikov. A note on computing certain answers to queries over incomplete databases. In AMW, 2017.","title":"A note on computing certain answers to queries over incomplete databases","authors":"Marcelo Arenas, Elena Botoeva, V Egor, Vladislav Kostylev, Ryzhikov","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bienvenu and Ortiz, 2015] Meghyn Bienvenu and Mag- dalena Ortiz. Ontology-mediated query answering with data-tractable description logics. In Reasoning Web, pages 218-307, 2015.","title":"Meghyn Bienvenu and Magdalena Ortiz. Ontology-mediated query answering with data-tractable description logics","authors":"Ortiz Bienvenu","year":"2015","venue":"Reasoning Web","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Buneman et al., 1991] Peter Buneman, Achim Jung, and Atsushi Ohori. Using powerdomains to generalize rela- tional databases. Theoretical Computer Science, 91(1):23- 55, 1991.","title":"Using powerdomains to generalize relational databases","authors":"Peter Buneman, Achim Jung, Atsushi Ohori","year":"1991","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Calì et al., 2003] Andrea Calì, Domenico Lembo, and Ric- cardo Rosati. Query rewriting and answering under con- straints in data integration systems. In IJCAI, pages 16-21, 2003.","title":"Query rewriting and answering under constraints in data integration systems","authors":"Andrea Calì, Domenico Lembo, Riccardo Rosati","year":"2003","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2003/3"},{"position":8,"raw":"[Calì et al., 2012] 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":"Andrea Calì, Georg Gottlob, Thomas Lukasiewicz","year":"2012","venue":"J. Web Sem","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Calvanese et al., 2007] Diego Calvanese, Giuseppe De Gi- acomo, Domenico Lembo, Maurizio Lenzerini, and Ric- cardo Rosati. Tractable reasoning and efficient query an- swering in description logics: The DL-Lite family. J. Au- tom. Reasoning, 39(3):385-429, 2007.","title":"Tractable reasoning and efficient query answering in description logics: The DL-Lite family","authors":"Calvanese","year":"2007","venue":"J. Autom. Reasoning","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Fagin et al., 2005] Ronald Fagin, Phokion G. Kolaitis, Re- nee J. Miller, and Lucian Popa. Data exchange: Seman- tics and query answering. Theoretical Computer Science, 336:89-124, 2005.","title":"Data exchange: Semantics and query answering","authors":"Ronald Fagin, G Phokion, Renee J Kolaitis, Lucian Miller, Popa","year":"2005","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Gheerbrant and Fontaine, 2014] Amélie Gheerbrant and Gaëlle Fontaine. Querying incomplete graphs with data. In AMW, 2014.","title":"Amélie Gheerbrant and Gaëlle Fontaine. Querying incomplete graphs with data","authors":"Fontaine Gheerbrant","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Gheerbrant et al., 2014] Amélie Gheerbrant, Leonid Libkin, and Cristina Sirangelo. Naïve evaluation of queries over incomplete databases. ACM Trans. Database Syst., 39(4):31:1-31:42, 2014.","title":"Amélie Gheerbrant, Leonid Libkin, and Cristina Sirangelo. Naïve evaluation of queries over incomplete databases","authors":"Gheerbrant","year":"2014","venue":"ACM Trans. Database Syst","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hell and Nešetřil, 2004] Pavol Hell and Jaroslav Nešetřil. Graphs and Homomorphisms. Oxford University Press, 2004.","title":"Pavol Hell and Jaroslav Nešetřil. Graphs and Homomorphisms","authors":"Nešetřil Hell","year":"2004","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hogan et al., 2014] Aidan Hogan, Marcelo Arenas, Alejan- dro Mallea, and Axel Polleres. Everything you always wanted to know about blank nodes. J. Web Sem., 27:42-69, 2014.","title":"Everything you always wanted to know about blank nodes","authors":"Aidan Hogan, Marcelo Arenas, Alejandro Mallea, Axel Polleres","year":"2014","venue":"J. Web Sem","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Imielinski and Lipski, 1984] Tomasz Imielinski and Witold Lipski. Incomplete information in relational databases. Journal of the ACM, 31(4):761-791, 1984.","title":"Incomplete information in relational databases","authors":"Lipski Imielinski, Tomasz Imielinski, Witold Lipski","year":"1984","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Lenzerini, 2002] Maurizio Lenzerini. Data integration: a theoretical perspective. In ACM Symposium on Principles of Database Systems (PODS), pages 233-246, 2002.","title":"Data integration: a theoretical perspective","authors":"Maurizio Lenzerini","year":"2002","venue":"ACM Symposium on Principles of Database Systems (PODS)","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Libkin, 2011] Leonid Libkin. Incomplete information and certain answers in general data models. In ACM Sympo- sium on Principles of Database Systems (PODS), pages 59-70, 2011.","title":"Leonid Libkin. Incomplete information and certain answers in general data models","authors":"Libkin","year":"2011","venue":"ACM Symposium on Principles of Database Systems (PODS)","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Libkin, 2016] Leonid Libkin. Certain answers as objects and knowledge. Artificial Intelligence, 232:1-19, 2016.","title":"Leonid Libkin. Certain answers as objects and knowledge","authors":"Libkin","year":"2016","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lipski, 1984] Witold Lipski. On relational algebra with marked nulls. In PODS, pages 201-203, 1984.","title":"On relational algebra with marked nulls","authors":"Witold Lipski","year":"1984","venue":"PODS","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Minker, 1982] Jack Minker. On indefinite databases and the closed world assumption. In CADE, pages 292-308, 1982.","title":"On indefinite databases and the closed world assumption","authors":"Jack Minker, Minker","year":"1982","venue":"CADE","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Nikolaou and Koubarakis, 2016] Charalampos Nikolaou and Manolis Koubarakis. Querying incomplete infor- mation in RDF with SPARQL. Artificial Intelligence, 237:138-171, 2016.","title":"Querying incomplete information in RDF with SPARQL","authors":"Charalampos Nikolaou, Manolis Koubarakis","year":"2016","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Reiter, 1977] Raymond Reiter. On closed world data bases. In Logic and Data Bases, pages 55-76, 1977.","title":"On closed world data bases","authors":"Raymond Reiter","year":"1977","venue":"Logic and Data Bases","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Reiter, 1980] Raymond Reiter. Equality and domain closure in first-order databases. Journal of the ACM, 27(2):235- 249, 1980.","title":"Equality and domain closure in first-order databases","authors":"Raymond Reiter","year":"1980","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Rosser and Schoenfeld, 1962] J. B. Rosser and L. Schoen- feld. Approximate formulas for some functions of prime numbers. Illinois J. Math., 6(2):64-94, 1962.","title":"Approximate formulas for some functions of prime numbers","authors":"Schoenfeld Rosser, J B Rosser, L Schoenfeld","year":"1962","venue":"Illinois J. Math","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Rounds, 1991] Bill Rounds. Situation-theoretic aspects of databases. In Situation Theory and Applications, vol- ume 26 of CSLI, pages 229-256. 1991.","title":"Bill Rounds. Situation-theoretic aspects of databases","authors":"Rounds","year":"1991","venue":"Situation Theory and Applications","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[ten Cate and Dalmau, 2015] Balder ten Cate and Víctor Dalmau. The product homomorphism problem and appli- cations. In ICDT, pages 161-176, 2015.","title":"Balder ten Cate and Víctor Dalmau. The product homomorphism problem and applications","authors":"Dalmau Cate","year":"2015","venue":"ICDT","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}