{"type":"ScholarlyArticle","title":"Best Answers over Incomplete Data : Complexity and First-Order Rewritings","authors":[{"name":"Amélie Gheerbrant","slug":"amelie-gheerbrant","given":"Amélie","family":"Gheerbrant","affiliation":"Université de Paris , IRIF , CNRS , F-75013 Paris , France"},{"name":"Cristina Sirangelo","slug":"cristina-sirangelo","given":"Cristina","family":"Sirangelo","affiliation":"Université de Paris , IRIF , CNRS , F-75013 Paris , France"}],"abstract":"Answering queries over incomplete data is ubiquitous in data management and in many AI applications that use query rewriting to take advantage of relational database technology. In these scenarios one lacks full information on the data but queries still need to be answered with certainty. The certainty aspect often makes query answering unfeasible except for restricted classes, such as unions of conjunctive queries. In addition often there are no, or very few certain answers, thus expensive computation is in vain. Therefore we study a relaxation of certain answers called best answers. They are defined as those answers for which there is no better one (that is, no answer true in more possible worlds). When certain answers exist the two notions coincide. We compare different ways of casting query answering as a decision problem and characterise its complexity for first-order queries, showing significant differences in the behavior of best and certain answers.We then restrict attention to best answers for unions of conjunctive queries and produce a practical algorithm for finding them based on query rewriting techniques.","doi":"10.24963/ijcai.2019/236","url":"https://ijcai.org/proceedings/2019/236","pdf":"https://ijcai.org/proceedings/2019/0236.pdf","markdown":"https://ijcai.org/proceedings/2019/236.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/236","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":236,"pages":{"first":1704,"last":1710},"keywords":["Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Logics for Knowledge Representation","Multidisciplinary Topics and Applications: Databases"],"videos":[],"references":[{"position":1,"raw":"[Abiteboul et al., 1991] Serge Abiteboul, Paris C. Kanel- lakis, and Gösta Grahne. On the representation and query- ing of sets of possible worlds. TCS, 78(1):158-187, 1991.","title":"On the representation and querying of sets of possible worlds","authors":"Serge Abiteboul, Paris C Kanellakis, Gösta Grahne","year":"1991","venue":"TCS","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Abiteboul et al., 1995] Serge Abiteboul, Richard Hull, and VictorVianu. Foundations of Databases. Addison-Wesley, Boston, MA, USA, 1995.","title":"Foundations of Databases","authors":"Serge Abiteboul, Richard Hull, Victorvianu","year":"1995","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Amendola and Libkin, 2018] Giovanni Amendola and Leonid Libkin. Explainable certain answers. In IJCAI, pages 1683-1690, Stockholm, Sweden, August 2018.","title":"Giovanni Amendola and Leonid Libkin. Explainable certain answers","authors":"Libkin Amendola","year":"2018","venue":"IJCAI","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Arenas et al., 2013] Marcelo Arenas, Jorge Pérez, and Juan L. Reutter. Data exchange beyond complete data. J. ACM, 60(4):28:1-28:59, 2013.","title":"Data exchange beyond complete data","authors":"Marcelo Arenas, Jorge Pérez, Juan L Reutter","year":"2013","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Arenas et al., 2014] Marcelo Arenas, Pablo Barcelo, Leonid Libkin, and Filip Murlak. Foundations of Data Exchange. Cambridge University Press, 2014.","title":"Foundations of Data Exchange","authors":"Marcelo Arenas, Pablo Barcelo, Leonid Libkin, Filip Murlak","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Barceló et al., 2014] Pablo Barceló, Leonid Libkin, and Miguel Romero. Efficient approximations of conjunctive queries. SIAM J. Comput., 43(3):1085-1130, 2014.","title":"Efficient approximations of conjunctive queries","authors":"Barceló","year":"2014","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bertossi, 2011] Leopoldo E. Bertossi. Database Repairing and Consistent Query Answering. Synthesis Lectures on Data Management. Morgan & Claypool Publishers, 2011.","title":"Database Repairing and Consistent Query Answering","authors":"Leopoldo E Bertossi","year":"2011","venue":"Synthesis Lectures on Data Management","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Bienvenu and Bourgaux, 2016] Meghyn Bienvenu and Camille Bourgaux. Inconsistency-tolerant querying of description logic knowledge bases. In Tutorial Lectures of RW Summer School, pages 156-202. LNCS, 2016.","title":"Inconsistency-tolerant querying of description logic knowledge bases","authors":"Bourgaux Bienvenu, Meghyn Bienvenu, Camille Bourgaux","year":"2016","venue":"Tutorial Lectures of RW Summer School","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Bienvenu and Ortiz, 2015] Meghyn Bienvenu and Mag- dalena Ortiz. Ontology-mediated query answering with data-tractable description logics. In Reasoning Web. Web Logic Rules -11th International Summer School, pages 218-307, Berlin, Germany, August 2015. Springer.","title":"Meghyn Bienvenu and Magdalena Ortiz. Ontology-mediated query answering with data-tractable description logics","authors":"Ortiz Bienvenu","year":"2015","venue":"Reasoning Web. Web Logic Rules -11th International Summer School","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Calì et al., 2003a] Andrea Calì, Domenico Lembo, and Ric- cardo Rosati. On the decidability and complexity of query answering over inconsistent and incomplete databases. In PODS, pages 260-271, June 2003.","title":"On the decidability and complexity of query answering over inconsistent and incomplete databases","authors":"Calì","year":"2003","venue":"PODS","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Calì et al., 2003b] Andrea Calì, Domenico Lembo, and Ric- cardo Rosati. Query rewriting and answering under con- straints in data integration systems. In IJCAI, pages 16-21, Acapulco, Mexico, August 2003.","title":"Query rewriting and answering under constraints in data integration systems","authors":"Calì","year":"2003","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2003/3"},{"position":12,"raw":"Morgan Kaufmann. [Calì et al., 2013]","title":null,"authors":"Morgan Kaufmann, . [ Calì","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"Andrea Calì, Diego Calvanese, and Mau- rizio Lenzerini. Rewrite and conquer: Dealing with in- tegrity constraints in data integrations. In Seminal Contri- butions to Information Systems Engineering, pages 353- 359, 2013.","title":"Rewrite and conquer: Dealing with integrity constraints in data integrations","authors":"Andrea Calì, Diego Calvanese, Maurizio Lenzerini","year":"2013","venue":"Seminal Contributions to Information Systems Engineering","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Calvanese et al., 2000] Diego Calvanese, Giuseppe De Gi- acomo, Maurizio Lenzerini, and Moshe Y. Vardi. What is view-based query rewriting? In KRDB, pages 17-27, Berlin, Germany, August 2000.","title":"What is view-based query rewriting?","authors":"Calvanese","year":"2000","venue":"KRDB","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Calvanese et al., 2006] Diego Calvanese, Giuseppe De Gi- acomo, Domenico Lembo, Maurizio Lenzerini, and Ric- cardo Rosati. Epistemic first-order queries over descrip- tion logic knowledge bases. In DL, Windermere, Lake District, UK, May-June 2006.","title":"Epistemic first-order queries over description logic knowledge bases","authors":"Calvanese","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Calvanese et al., 2007] Diego Calvanese, Giuseppe De Gi- acomo, Maurizio Lenzerini, and Moshe Y. Vardi. View- based query processing: On the relationship between rewriting, answering and losslessness. TCS, 371(3):169- 182, March 2007.","title":"Viewbased query processing: On the relationship between rewriting, answering and losslessness","authors":"Calvanese","year":"2007","venue":"TCS","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Eiter and Gottlob, 1997] Thomas Eiter and Georg Gottlob. The complexity class theta 2 p : Recent results and applica- tions in AI and modal logic. In FCT, pages 1-18, Kraków, Poland, September 1997. Springer.","title":"The complexity class theta 2 p : Recent results and applications in AI and modal logic","authors":"Thomas Eiter, Georg Gottlob","year":"1997","venue":"FCT","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Fagin et al., 2005] Ronald Fagin, Phokion G. Kolaitis, and Lucian Popa. Data exchange: getting to the core. ACM TODS, 30(1):174-210, 2005.","title":"Data exchange: getting to the core","authors":"Ronald Fagin, G Phokion, Lucian Kolaitis, Popa","year":"2005","venue":"ACM TODS","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Francis et al., 2015] Nadime Francis, Luc Segoufin, and Cristina Sirangelo. Datalog rewritings of regular path queries using views. Logical Methods in Computer Sci- ence, 11(4), 2015.","title":"Datalog rewritings of regular path queries using views","authors":"Francis","year":"2015","venue":"Logical Methods in Computer Science","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Geerts et al., 2013] Floris Geerts, Giansalvatore Mecca, Paolo Papotti, and Donatello Santoro. The LLUNATIC data-cleaning framework. PVLDB, 6(9):625-636, 2013.","title":"The LLUNATIC data-cleaning framework","authors":"Floris Geerts, Giansalvatore Mecca, Paolo Papotti, Donatello Santoro","year":"2013","venue":"PVLDB","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Gheerbrant and Libkin, 2015] Amélie Gheerbrant and Leonid Libkin. Certain answers over incomplete xml documents: Extending tractability boundary. ACM ToCS, 57(4):892-926, July 2015.","title":"Amélie Gheerbrant and Leonid Libkin. Certain answers over incomplete xml documents: Extending tractability boundary","authors":"Libkin Gheerbrant","year":"2015","venue":"ACM ToCS","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Gottlob et al., 2015] Georg Gottlob, Marco Manna, and An- dreas Pieris. Polynomial rewritings for linear existential rules. In IJCAI, pages 2992-2998, Buenos Aires, Ar- gentina, August 2015. AAAI Press.","title":"Polynomial rewritings for linear existential rules","authors":"Gottlob","year":"2015","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/423"},{"position":23,"raw":"[Gottlob, 1995] Georg Gottlob. NP trees and Carnap's modal logic. Journal of the ACM, 42(2):421-457, March 1995.","title":"NP trees and Carnap's modal logic","authors":"Georg Gottlob, Gottlob","year":"1995","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Imieliński and Lipski, 1984] Tomasz Imieliński and Witold Lipski. Incomplete information in relational databases. Journal of the ACM, 31(4):761-791, Oct 1984.","title":"Tomasz Imieliński and Witold Lipski. Incomplete information in relational databases","authors":"Lipski Imieliński","year":"1984","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Lenzerini, 2002] Maurizio Lenzerini. Data integration: A theoretical perspective. In ACM PODS, pages 233-246, Madison, USA, June 2002.","title":"Data integration: A theoretical perspective","authors":"Maurizio Lenzerini","year":"2002","venue":"ACM PODS","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Libkin, 2018a] Leonid Libkin. Certain answers as objects of knowledge. Artificial Intellligence, 232:195-207, 2018.","title":"Certain answers as objects of knowledge","authors":"Leonid Libkin, Libkin","year":"2018","venue":"Artificial Intellligence","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Libkin, 2018b] Leonid Libkin. Certain answers meet zero- one laws. In ACM PODS, pages 1-19, Houston, USA, June 2018.","title":"Certain answers meet zeroone laws","authors":"Leonid Libkin, Libkin","year":"2018","venue":"ACM PODS","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Lipski, 1984] Witold Lipski. On relational algebra with marked nulls. In PODS, pages 201-203, Waterloo, On- tario, Canada, April 1984. ACM.","title":"On relational algebra with marked nulls","authors":"Witold Lipski","year":"1984","venue":"PODS","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Rothe, 2003] Jörg Rothe. Exact complexity of exact-four- colorability. Inf. Process. Lett., 87(1):7-12, 2003.","title":"Exact complexity of exact-fourcolorability","authors":"Jörg Rothe, Rothe","year":"2003","venue":"Inf. Process. Lett","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[van der Meyden, 1998] Ron van der Meyden. Logical ap- proaches to incomplete information: a survey. In Logics for databases and information systems, pages 307-356, Norwell, MA, USA, 1998. Kluwer Academic Publishers.","title":"Ron van der Meyden. Logical approaches to incomplete information: a survey","authors":"Van Der Meyden","year":"1998","venue":null,"doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Wagner, 1990] Klaus W. Wagner. Bounded query classes. SIAM J. Comput., 19(5):833-846, 1990.","title":"Bounded query classes","authors":"Klaus W Wagner","year":"1990","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}