A distance-based framework for inconsistency-tolerant reasoning and inconsistency measurement in DL-Lite

In this paper, we present a distance-based framework for DL-Lite based on the notion of features. Within this framework, we propose a distance-based paraconsistent semantics for DL-Lite where meaningful conclusions can be rationally drawn even from an inconsistent knowledge base and we develop a distance-based inconsistency measurement for DL-Lite to provide more informative metrics which can tell the differences between axioms causing inconsistency and among inconsistent knowledge. Furthermore, we investigate several important logical properties (e.g., consistency preservation, closure consistency, splitting property etc.) of the entailment relation based on the new semantics and show its advantages in non-monotonic reasoning for DL-Lite. Finally, we show that our two distance-based inconsistency measures are basic inconsistency measures where some good properties hold such as Free Axiom Independence and Dominance of inconsistency etc.

[1]  Bijan Parsia,et al.  Repairing Unsatisfiable Concepts in OWL Ontologies , 2006, ESWC.

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

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

[4]  Lakhdar Sais,et al.  On Structure-Based Inconsistency Measures and Their Computations via Closed Set Packing , 2015, AAMAS.

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

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

[7]  Riccardo Rosati,et al.  Tractable Approximations of Consistent Query Answering for Robust Ontology-based Data Access , 2013, IJCAI.

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

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

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

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

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

[13]  James A. Hendler,et al.  The Semantic Web" in Scientific American , 2001 .

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

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

[16]  Yue Ma,et al.  Inconsistency measurement thanks to mus decomposition , 2014, AAMAS.

[17]  Weiru Liu,et al.  From inconsistency handling to non-canonical requirements management: A logical perspective , 2013, Int. J. Approx. Reason..

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

[19]  Guilin Qi,et al.  Computing Inconsistency Measurements under Multi-Valued Semantics by Partial Max-SAT Solvers , 2010, KR.

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

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

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

[23]  Pascal Hitzler,et al.  Paraconsistent Reasoning for OWL 2 , 2009, RR.

[24]  Jianfeng Du,et al.  Towards Tractable and Practical ABox Abduction over Inconsistent Description Logic Ontologies , 2015, AAAI.

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

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

[27]  John Grant,et al.  Measuring inconsistency in knowledgebases , 2006, Journal of Intelligent Information Systems.

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

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

[30]  G Stix,et al.  The mice that warred. , 2001, Scientific American.

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

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

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

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

[35]  Kedian Mu,et al.  Responsibility for inconsistency , 2015, Int. J. Approx. Reason..

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

[37]  Anthony Hunter,et al.  On the measure of conflicts: Shapley Inconsistency Values , 2010, Artif. Intell..

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

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

[40]  Kevin McAreavey,et al.  Computational approaches to finding and measuring inconsistency in arbitrary knowledge bases , 2014, Int. J. Approx. Reason..

[41]  Guilin Qi,et al.  Measuring Incoherence in Description Logic-Based Ontologies , 2007, ISWC/ASWC.

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

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

[44]  Xi Deng,et al.  Measuring Inconsistencies in Ontologies , 2007, ESWC.

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

[46]  Weiru Liu,et al.  Imprecise probabilistic query answering using measures of ignorance and degree of satisfaction , 2012, Annals of Mathematics and Artificial Intelligence.

[47]  Anthony Hunter,et al.  Measuring Inconsistency through Minimal Inconsistent Sets , 2008, KR.

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

[49]  Sébastien Konieczny,et al.  On the Logic of Merging , 1998, KR.

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

[51]  Kewen Wang,et al.  Approaches to measuring inconsistency for stratified knowledge bases , 2014, Int. J. Approx. Reason..

[52]  Alexander Borgida,et al.  On the relationship between description logic and predicate logic queries , 1994, CIKM '94.

[53]  Guilin Qi,et al.  Measuring Inconsistency in DL-Lite Ontologies , 2009, 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology.

[54]  Xiaowang Zhang,et al.  Forgetting for distance-based reasoning and repair in DL-Lite , 2016, Knowl. Based Syst..

[55]  Stefan Schlobach.  Diagnosing Terminologies , 2005, AAAI.

[56]  François Goasdoué,et al.  Querying Inconsistent Description Logic Knowledge Bases under Preferred Repair Semantics , 2014, Description Logics.

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

[58]  Weiru Liu,et al.  Measuring the blame of each formula for inconsistent prioritized knowledge bases , 2012, J. Log. Comput..

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

[60]  Guilin Qi,et al.  Computing inconsistency measure based on paraconsistent semantics , 2011, J. Log. Comput..

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