{"type":"ScholarlyArticle","title":"DatalogMTL: Computational Complexity and Expressive Power","authors":[{"name":"Przemysław A. Wałęga","slug":"przemys-aw-a-wa-ega","given":"Przemysław A.","family":"Wałęga","affiliation":"Department of Computer Science , University of Oxford , UK; Institute of Philosophy , University of Warsaw , Poland"},{"name":"Bernardo Cuenca Grau","slug":"bernardo-cuenca-grau","given":"Bernardo Cuenca","family":"Grau","affiliation":"Department of Computer Science , University of Oxford , UK"},{"name":"Mark Kaminski","slug":"mark-kaminski","given":"Mark","family":"Kaminski","affiliation":"Department of Computer Science , University of Oxford , UK"},{"name":"Egor V. Kostylev","slug":"egor-v-kostylev","given":"Egor V.","family":"Kostylev","affiliation":"Department of Computer Science , University of Oxford , UK"}],"abstract":"We study the complexity and expressive power of DatalogMTL - a knowledge representation language that extends Datalog with operators from metric temporal logic (MTL) and which has found applications in ontology-based data access and stream reasoning. We establish tight PSpace data complexity bounds and also show that DatalogMTL extended with negation on input predicates can express all queries in PSpace; this implies that MTL operators add significant expressive power to Datalog. Furthermore, we provide tight combined complexity bounds for the forward-propagating fragment of DatalogMTL, which was proposed in the context of stream reasoning, and show that it is possible to express all PSpace queries in the fragment extended with the falsum predicate.","doi":"10.24963/ijcai.2019/261","url":"https://ijcai.org/proceedings/2019/261","pdf":"https://ijcai.org/proceedings/2019/0261.pdf","markdown":"https://ijcai.org/proceedings/2019/261.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/261","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":261,"pages":{"first":1886,"last":1892},"keywords":["Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning","Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Logics for Knowledge Representation","Knowledge Representation and Reasoning: Non-classical Logics for Knowledge Representation"],"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":"[Alur and Henzinger, 1993] Rajeev Alur and Thomas A. Henzinger. Real-time logics: Complexity and expressive- ness. Inf. Comput., 104(1):35-77, 1993.","title":"Real-time logics: Complexity and expressiveness","authors":"Rajeev Alur, Thomas A Henzinger","year":"1993","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Alur et al., 1996] Rajeev Alur, Tomás Feder, and Thomas A Henzinger. The benefits of relaxing punctuality. J. ACM, 43(1):116-146, 1996.","title":"The benefits of relaxing punctuality","authors":"Rajeev Alur, Tomás Feder, Thomas A Henzinger","year":"1996","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Artale et al., 2017] Alessandro Artale, Roman Kontchakov, Alisa Kovtunova, Vladislav Ryzhikov, Frank Wolter, and Michael Zakharyaschev. Ontology-mediated query an- swering over temporal data: A survey (invited talk). In LIPIcs-Leibniz International Proceedings in Informatics, volume 90, 2017.","title":"Ontology-mediated query answering over temporal data: A survey (invited talk)","authors":"Alessandro Artale, Roman Kontchakov, Alisa Kovtunova, Vladislav Ryzhikov, Frank Wolter, Michael Zakharyaschev","year":"2017","venue":"LIPIcs-Leibniz International Proceedings in Informatics","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Baldor and Niu, 2012] Kevin Baldor and Jianwei Niu. Monitoring dense-time, continuous-semantics, metric temporal logic. In RV, pages 245-259, 2012.","title":"Monitoring dense-time, continuous-semantics, metric temporal logic","authors":"Kevin Baldor, Jianwei Niu","year":"2012","venue":"RV","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Basin et al., 2018] David Basin, Felix Klaedtke, and Eugen Zȃlinescu. Algorithms for monitoring real-time properties. Acta Inform., 55(4):309-338, 2018.","title":"Algorithms for monitoring real-time properties","authors":"David Basin, Felix Klaedtke, Eugen Zȃlinescu","year":"2018","venue":"Acta Inform","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Brandt et al., 2017] Sebastian Brandt, R Kontchakov, V Ryzhikov, G Xiao, and M Zakharyaschev. Ontology- based data access with a Horn fragment of metric temporal logic. In AAAI, pages 1070-1076. AAAI Press, 2017.","title":"Ontologybased data access with a Horn fragment of metric temporal logic","authors":"Sebastian Brandt, R Kontchakov, V Ryzhikov, G Xiao, M Zakharyaschev","year":"2017","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Brandt et al., 2018] Sebastian Brandt, Elem Güzel Kalaycı, Vladislav Ryzhikov, Guohui Xiao, and Michael Za- kharyaschev. Querying log data with metric temporal logic. J. Artif. Intell. Res., 62:829-877, 2018.","title":"Querying log data with metric temporal logic","authors":"Sebastian Brandt, Elem Güzel Kalaycı, Vladislav Ryzhikov, Guohui Xiao, Michael Zakharyaschev","year":"2018","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Dantsin et al., 2001] Evgeny Dantsin, Thomas Eiter, Georg Gottlob, and Andrei Voronkov. Complexity and expres- sive power of logic programming. ACM Comput. Surv., 33(3):374-425, 2001.","title":"Complexity and expressive power of logic programming","authors":"Evgeny Dantsin, Thomas Eiter, Georg Gottlob, Andrei Voronkov","year":"2001","venue":"ACM Comput. Surv","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Doherty et al., 2009] Patrick Doherty, Jonas Kvarnström, and Fredrik Heintz. A temporal logic-based planning and execution monitoring framework for unmanned aircraft systems. Auton. Agents Multi-Agent Syst., 19(3):332-377, 2009.","title":"A temporal logic-based planning and execution monitoring framework for unmanned aircraft systems","authors":"Patrick Doherty, Jonas Kvarnström, Fredrik Heintz","year":"2009","venue":"Auton. Agents Multi-Agent Syst","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Ho et al., 2014] Hsi-Ming Ho, Joël Ouaknine, and James Worrell. Online monitoring of metric temporal logic. In RV, pages 178-192, 2014.","title":"Online monitoring of metric temporal logic","authors":"Ming Hsi, Joël Ho, James Ouaknine, Worrell","year":"2014","venue":"RV","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Immerman, 1999] Neil Immerman. Descriptive Complex- ity. Springer, 1999.","title":"Descriptive Complexity","authors":"Neil Immerman","year":"1999","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Kikot et al., 2018] Stanislav Kikot, Vladislav Ryzhikov, Przemysław Andrzej Wałęga, and Michael Zakharyaschev. On the data complexity of ontology-mediated queries with MTL operators over timed words. In DL, 2018.","title":"On the data complexity of ontology-mediated queries with MTL operators over timed words","authors":"Stanislav Kikot, Vladislav Ryzhikov, Andrzej Przemysław, Michael Wałęga, Zakharyaschev","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Ničković and Piterman, 2010] Dejan Ničković and Nir Piterman. From MTL to deterministic timed automata. In FORMATS, pages 152-167, 2010.","title":"From MTL to deterministic timed automata","authors":"Piterman Ničković, Dejan Ničković, Nir Piterman","year":"2010","venue":"FORMATS","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Thati and Roşu, 2005] Prasanna Thati and Grigore Roşu. Monitoring algorithms for metric temporal logic specifica- tions. Electron. Notes Theor. Comput. Sci., 113:145-162, 2005.","title":"Monitoring algorithms for metric temporal logic specifications","authors":"Prasanna Thati, Grigore Roşu","year":"2005","venue":"Electron. Notes Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Wałęga et al., 2019] Przemysław Andrzej Wałęga, Bernardo Cuenca Grau, and Mark Kaminski. Rea- soning over streaming data in metric temporal datalog. In AAAI, pages 1941-1948, 2019.","title":"Reasoning over streaming data in metric temporal datalog","authors":"Andrzej Przemysław, Bernardo Cuenca Wałęga, Mark Grau, Kaminski","year":"2019","venue":"AAAI","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}