Reasoning with Probabilistic Ontologies

Modeling real world domains requires ever more frequently to represent uncertain information. The DISPONTE semantics for probabilistic description logics allows to annotate axioms of a knowledge base with a value that represents their probability. In this paper we discuss approaches for performing inference from probabilistic ontologies following the DISPONTE semantics. We present the algorithm BUNDLE for computing the probability of queries. BUNDLE exploits an underlying Description Logic reasoner, such as Pellet, in order to find explanations for a query. These are then encoded in a Binary Decision Diagram that is used for computing the probability of the query.

[1]  Thomas Lukasiewicz,et al.  Expressive probabilistic description logics , 2008, Artif. Intell..

[2]  Rafael Peñaloza,et al.  Axiom Pinpointing is Hard , 2009, Description Logics.

[3]  Aditya Kalyanpur,et al.  Debugging and Repair of OWL Ontologies , 2006 .

[4]  Bijan Parsia,et al.  Finding All Justifications of OWL DL Entailments , 2007, ISWC/ASWC.

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

[6]  Yoshitaka Kameya,et al.  Parameter Learning of Logic Programs for Symbolic-Statistical Modeling , 2001, J. Artif. Intell. Res..

[7]  David Poole,et al.  The Independent Choice Logic for Modelling Multiple Agents Under Uncertainty , 1997, Artif. Intell..

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

[9]  Fabrizio Riguzzi,et al.  The PITA system: Tabling and answer subsumption for reasoning under uncertainty , 2011, Theory Pract. Log. Program..

[10]  Evelina Lamma,et al.  Learning Probabilistic Description Logics , 2014, URSW.

[11]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

[12]  Evelina Lamma,et al.  Probabilistic Description Logics under the distribution semantics , 2015, Semantic Web.

[13]  Nils J. Nilsson,et al.  Probabilistic Logic * , 2022 .

[14]  Ian Horrocks,et al.  Description Logics , 2008, Handbook of Knowledge Representation.

[15]  Pavel Klinov Pronto: A Non-monotonic Probabilistic Description Logic Reasoner , 2008, ESWC.

[16]  Yarden Katz,et al.  Pellet: A practical OWL-DL reasoner , 2007, J. Web Semant..

[17]  Christophe Bérenguer,et al.  A practical comparison of methods to assess sum-of-products , 2003, Reliab. Eng. Syst. Saf..

[18]  Evelina Lamma,et al.  BUNDLE: A Reasoner for Probabilistic Ontologies , 2013, RR.

[19]  Stefan Schlobach,et al.  Non-Standard Reasoning Services for the Debugging of Description Logic Terminologies , 2003, IJCAI.

[20]  Pierre Marquis,et al.  A Knowledge Compilation Map , 2002, J. Artif. Intell. Res..

[21]  Jean Christoph Jung,et al.  Ontology-Based Access to Probabilistic Data with OWL QL , 2012, SEMWEB.

[22]  Adnan Darwiche,et al.  On probabilistic inference by weighted model counting , 2008, Artif. Intell..

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

[24]  Fabrizio Riguzzi,et al.  Expectation maximization over binary decision diagrams for probabilistic logic programs , 2013, Intell. Data Anal..

[25]  Evelina Lamma,et al.  Semantics and Inference for Probabilistic Description Logics , 2013, URSW.

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

[27]  Beate Bollig,et al.  Improving the Variable Ordering of OBDDs Is NP-Complete , 1996, IEEE Trans. Computers.

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

[29]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[30]  Evelina Lamma,et al.  A Description Logics Tableau Reasoner in Prolog , 2013, CILC.

[31]  Fabrizio Riguzzi,et al.  Structure learning of probabilistic logic programs by searching the clause space , 2013, Theory and Practice of Logic Programming.

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

[33]  Fabrizio Riguzzi,et al.  Experimentation of an expectation maximization algorithm for probabilistic logic programs , 2012, Intelligenza Artificiale.

[34]  Umberto Straccia,et al.  Managing Uncertainty and Vagueness in Description Logics, Logic Programs and Description Logic Programs , 2008, Reasoning Web.

[35]  Rafael Peñaloza,et al.  Pinpointing in the Description Logic EL , 2007, Description Logics.

[36]  Rafael Peñaloza,et al.  Complexity of Axiom Pinpointing in the DL-Lite Family , 2010, Description Logics.

[37]  Pavel Klinov,et al.  A Hybrid Method for Probabilistic Satisfiability , 2011, CADE.

[38]  Bijan Parsia,et al.  Explaining Inconsistencies in OWL Ontologies , 2009, SUM.

[39]  Shaul Markovitch,et al.  Learning to Order BDD Variables in Verification , 2011, J. Artif. Intell. Res..

[40]  Henry A. Kautz,et al.  Performing Bayesian Inference by Weighted Model Counting , 2005, AAAI.

[41]  Evelina Lamma,et al.  Epistemic and Statistical Probabilistic Ontologies , 2012, URSW.