Forgetting for distance-based reasoning and repair in DL-Lite

In this paper, we present a forgetting-based approach to handling inconsistency in DL-Lite. Our proposed approach cannot only characterize distance-based reasoning, which is proven to rationally draw meaningful conclusions even from inconsistent DL-Lite knowledge bases but also recovery the consistency of DL-Lite knowledge bases. We first present vectors forgetting for DL-Lite by extending predicates forgetting in DL-Lite and show the predicates to be forgotten which are obtained by computing minimal hitting sets. Moreover, we develop algorithms to compute those predicates by employing Reiter's HS-tree method and then analyze the computational complexity of those proposed algorithms. Finally, we implement our proposed algorithms and evaluate them on both consistent and inconsistent ontologies. Besides, we discuss some applications of vectors forgetting in privacy protection.

[1]  Pascal Hitzler,et al.  Distance-based Measures of Inconsistency and Incoherency for Description Logics , 2010, Description Logics.

[2]  Kewen Wang,et al.  A New Approach to Knowledge Base Revision in DL-Lite , 2010, AAAI.

[3]  Torsten Schaub,et al.  Inconsistency Tolerance , 2005, Lecture Notes in Computer Science.

[4]  Huiying Li,et al.  Parallel mining of OWL 2 EL ontology from large linked datasets , 2015, Knowl. Based Syst..

[5]  Ofer Arieli,et al.  Distance-based paraconsistent logics , 2008, Int. J. Approx. Reason..

[6]  Man Zhu,et al.  Measuring effectiveness of ontology debugging systems , 2014, Knowl. Based Syst..

[7]  Xin Wang,et al.  PROSE: A Plugin-Based Paraconsistent OWL Reasoner , 2015, JIST.

[8]  Xiaowang Zhang,et al.  An argumentation framework for description logic ontology reasoning and management , 2012, Journal of Intelligent Information Systems.

[9]  Jianfeng Du,et al.  Weight-based consistent query answering over inconsistent $${\mathcal {SHIQ}}$$ knowledge bases , 2012, Knowledge and Information Systems.

[10]  Stefan Schlobach,et al.  Diagnosing Terminologies , 2005, AAAI.

[11]  Qingguo Li,et al.  Reasoning with inconsistencies in hybrid MKNF knowledge bases , 2013, Log. J. IGPL.

[12]  Marco Schaerf,et al.  Tractable Reasoning via Approximation , 1995, Artif. Intell..

[13]  Riccardo Rosati,et al.  Evaluation of Techniques for Inconsistency Handling in OWL 2 QL Ontologies , 2012, International Semantic Web Conference.

[14]  James A. Hendler,et al.  Debugging unsatisfiable classes in OWL ontologies , 2005, J. Web Semant..

[15]  Jeff Z. Pan,et al.  Finding Maximally Satisfiable Terminologies for the Description Logic ALC , 2006, AAAI.

[16]  Jie Lu,et al.  A state-based knowledge representation approach for information logical inconsistency detection in warning systems , 2010, Knowl. Based Syst..

[17]  Guilin Qi,et al.  Approximating Model-Based ABox Revision in DL-Lite: Theory and Practice , 2015, AAAI.

[18]  Jan Van den Bussche,et al.  Inconsistency-tolerant reasoning with OWL DL , 2014, Int. J. Approx. Reason..

[19]  Guilin Qi,et al.  A Distance-Based Paraconsistent Semantics for DL-Lite , 2015, KSEM.

[20]  Chao Wang,et al.  Integration of Ontology Data through Learning Instance Matching , 2006, 2006 IEEE/WIC/ACM International Conference on Web Intelligence (WI 2006 Main Conference Proceedings)(WI'06).

[21]  Maurizio Lenzerini,et al.  Inconsistency-Tolerant Semantics for Description Logics , 2010, RR.

[22]  Umberto Straccia,et al.  Reasoning within Fuzzy Description Logics , 2011, J. Artif. Intell. Res..

[23]  Yan Zhang,et al.  Knowledge forgetting: Properties and applications , 2009, Artif. Intell..

[24]  Li Ma,et al.  Scalable Cleanup of Information Extraction Data Using Ontologies , 2007, ISWC/ASWC.

[25]  Boris Motik,et al.  OWL 2: The next step for OWL , 2008, J. Web Semant..

[26]  Riccardo Rosati,et al.  On the Complexity of Dealing with Inconsistency in Description Logic Ontologies , 2011, IJCAI.

[27]  Frank Wolter,et al.  Can You Tell the Difference Between DL-Lite Ontologies? , 2008, KR.

[28]  Pascal Hitzler,et al.  Paraconsistent OWL and related logics , 2013, Semantic Web.

[29]  Diego Calvanese,et al.  The DL-Lite Family and Relations , 2009, J. Artif. Intell. Res..

[30]  Norihiro Kamide,et al.  Embedding-based approaches to paraconsistent and temporal description logics , 2012, J. Log. Comput..

[31]  Anna Zamansky,et al.  What Is an Ideal Logic for Reasoning with Inconsistency? , 2011, IJCAI.

[32]  Ian Horrocks,et al.  Ontologies and the semantic web , 2008, CACM.

[33]  Bernardo Cuenca Grau.  Privacy in ontology-based information systems: A pending matter , 2010, Semantic Web.

[34]  Sébastien Konieczny,et al.  Distance Based Merging: A General Framework and some Complexity Results , 2002, KR.

[35]  Kewen Wang,et al.  Semantic forgetting in answer set programming , 2008, Artif. Intell..

[36]  Maurice Bruynooghe,et al.  Distance semantics for database repair , 2007, Annals of Mathematics and Artificial Intelligence.

[37]  Pierre Marquis,et al.  Reasoning under inconsistency: A forgetting-based approach , 2010, Artif. Intell..

[38]  Boris Konev,et al.  Forgetting and Uniform Interpolation in Large-Scale Description Logic Terminologies , 2009, IJCAI.

[39]  Jianfeng Du,et al.  Computing minimum cost diagnoses to repair populated DL-based ontologies , 2008, WWW.

[40]  Elizabeth Chang,et al.  Ontology usage analysis in the ontology lifecycle: A state-of-the-art review , 2015, Knowl. Based Syst..

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

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

[43]  Jianfeng Du,et al.  Weight-based consistent query answering over inconsistent SHIQ knowledge bases , .

[44]  Diego Calvanese,et al.  DL-Lite in the Light of First-Order Logic , 2007, AAAI.

[45]  Samantha Bail,et al.  Toward cognitive support for OWL justifications , 2013, Knowl. Based Syst..

[46]  Raymond Reiter,et al.  A Theory of Diagnosis from First Principles , 1986, Artif. Intell..

[47]  Jeff Z. Pan,et al.  Forgetting for knowledge bases in DL-Lite , 2010, Annals of Mathematics and Artificial Intelligence.

[48]  Guilin Qi,et al.  Contraction and Revision over DL-Lite TBoxes , 2014, AAAI.

[49]  Frank van Harmelen,et al.  Reasoning with Inconsistent Ontologies , 2005, IJCAI.

[50]  Kewen Wang,et al.  DL-Lite Ontology Revision Based on An Alternative Semantic Characterization , 2015, ACM Trans. Comput. Log..