Probabilistic Datalog+/- under the Distribution Semantics

We apply the distribution semantics for probabilistic ontologies (named DISPONTE) to the Datalog+/language. In DISPONTE the formulas of a probabilistic ontology can be annotated with an epistemic or a statistical probability. The epistemic probability represents a degree of confidence in the formula, while the statistical probability considers the populations to which the formula is applied. The probability of a query is defined in terms of finite set of finite explanations for the query, where an explanation is a set of possibly instantiated formulas that is sufficient for entailing the query. The probability of a query is computed from the set of explanations by making them mutually exclusive. We also compare the DISPONTE approach for Datalog+/ontologies with that of Probabilistic Datalog+/-, where an ontology is composed of a Datalog+/theory whose formulas are associated to an assignment of values for the random variables of a companion Markov Logic Network.

[1]  Luc De Raedt,et al.  On the implementation of the probabilistic logic programming language ProbLog , 2010, Theory and Practice of Logic Programming.

[2]  Georg Gottlob,et al.  Answering Threshold Queries in Probabilistic Datalog+/- Ontologies , 2011, SUM.

[3]  David Poole,et al.  Abducing through negation as failure: stable models within the independent choice logic , 2000, J. Log. Program..

[4]  Andrea Calì,et al.  Tractable Query Answering over Ontologies with Datalog+/- , 2009, Description Logics.

[5]  Umberto Straccia,et al.  Managing uncertainty and vagueness in description logics for the Semantic Web , 2008, J. Web Semant..

[6]  Andrea Calì,et al.  Taming the Infinite Chase: Query Answering under Expressive Relational Constraints , 2008, Description Logics.

[7]  Joseph Y. Halpern.  An Analysis of First-Order Logics of Probability , 1989, IJCAI.

[8]  Diego Calvanese,et al.  Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family , 2007, Journal of Automated Reasoning.

[9]  Andrea Calì,et al.  A general Datalog-based framework for tractable query answering over ontologies , 2012, J. Web Semant..

[10]  Evelina Lamma,et al.  A Distribution Semantics for Probabilistic Ontologies , 2011, URSW.

[11]  Georg Gottlob,et al.  Conjunctive Query Answering in Probabilistic Datalog+/- Ontologies , 2011, RR.

[12]  Andrea Calì,et al.  Datalog+/-: A Family of Logical Knowledge Representation and Query Languages for New Applications , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[13]  Andrea Calì,et al.  A general datalog-based framework for tractable query answering over ontologies , 2009, SEBD.

[14]  Maurice Bruynooghe,et al.  Logic programs with annotated disjunctions , 2004, NMR.

[15]  Thomas Lukasiewicz,et al.  Uncertainty Reasoning for the Semantic Web I, ISWC International Workshops, URSW 2005-2007, Revised Selected and Invited Papers , 2008, URSW.

[16]  Fabrizio Riguzzi,et al.  Extended semantics and inference for the Independent Choice Logic , 2009, Log. J. IGPL.

[17]  Taisuke Sato,et al.  A Statistical Learning Method for Logic Programs with Distribution Semantics , 1995, ICLP.

[18]  Matthew Richardson,et al.  Markov logic networks , 2006, Machine Learning.

[19]  Kathryn B. Laskey,et al.  Uncertainty Reasoning for the World Wide Web: Report on the URW3-XG Incubator Group , 2008, URSW.

[20]  Luc De Raedt,et al.  ProbLog: A Probabilistic Prolog and its Application in Link Discovery , 2007, IJCAI.