Tableau-based revision for expressive description logics with individuals

Abstract Our understanding of an application domain evolves over time. If we consider an ontology as a set of semantic constraints which describes our understanding of an application domain, ontologies must be revised. Indeed, adding a new semantic constraint to an ontology may make it inconsistent. To restore consistency with minimal loss of semantics, we would change other semantic constraints of the ontology such that the resulting ontology is semantically as close as possible to the initial ontology. To be able to say that an ontology is semantically close to another one, it is needed to define a distance over finite structures representing models, called completion graphs, which characterize the semantics of an ontology. In this paper we present a tableau algorithm for building such completion graphs of an ontology expressed in the description logic SHIQ with individuals. Based on the distance defined over completion graphs, we introduce a revision operation applied to a SHIQ ontology with a set of new semantic constraints. This revision operation computes the completion graphs that a revised ontology should admit. However, there does not always exist an ontology expressible in SHIQ from which a tableau algorithm generates exactly a given set of completion graphs. This leads us to introduce the notion of upper approximation ontology from which a tableau algorithm can generate the smallest set of completion graphs including a given set of completion graphs. This notion allows us to design an algorithm for constructing a revised ontology from an initial ontology with a set of new semantic constraints. We also implement the proposed algorithms with optimizations and report some experimental results to show that a model-based approach to revision of expressive ontologies is practicable.

[1]  Ian Horrocks,et al.  FaCT++ Description Logic Reasoner: System Description , 2006, IJCAR.

[2]  Georg Gottlob,et al.  On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals , 1992, Artif. Intell..

[3]  Ian Horrocks,et al.  Practical Reasoning for Expressive Description Logics , 1999, LPAR.

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

[5]  Ian Horrocks,et al.  Optimised Reasoning for SHIQ , 2002, ECAI.

[6]  Birte Glimm,et al.  Konclude: System description , 2014, J. Web Semant..

[7]  Myriam Lamolle,et al.  Tableau-Based Revision over SHIQ TBoxes , 2015, LPAR.

[8]  Maurizio Lenzerini,et al.  On the Approximation of Instance Level Update and Erasure in Description Logics , 2007, AAAI.

[9]  Boris Motik,et al.  Optimized Description Logic Reasoning via Core Blocking , 2010, IJCAR.

[10]  Thomas Caridroit,et al.  On Distances Between KD45n Kripke Models and Their Use for Belief Revision , 2016, ECAI.

[11]  Franz Baader,et al.  An Overview of Tableau Algorithms for Description Logics , 2001, Stud Logica.

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

[13]  Guilin Qi,et al.  DL-Lite Contraction and Revision , 2016, J. Artif. Intell. Res..

[14]  Guilin Qi,et al.  Instance-Driven Ontology Evolution in DL-Lite , 2015, AAAI.

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

[16]  Guilin Qi,et al.  Knowledge Base Revision in Description Logics , 2006, JELIA.

[17]  Mukesh Dalal,et al.  Investigations into a Theory of Knowledge Base Revision , 1988, AAAI.

[18]  Jérôme Euzenat,et al.  Revision in networks of ontologies , 2015, Artif. Intell..

[19]  Evgeny Kharlamov,et al.  Ontology Evolution Under Semantic Constraints , 2012, KR.

[20]  Diego Calvanese,et al.  Data Complexity of Query Answering in Description Logics , 2006, Description Logics.

[21]  Diego Calvanese,et al.  Evolution of DL-Lite Knowledge Bases , 2010, SEMWEB.

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

[23]  Ken Satoh.  Nonmonotonic Reasoning by Minimal Belief Revision , 1988, FGCS.

[24]  Stephan Tobies,et al.  The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics , 2011, ArXiv.

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

[26]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[27]  Diego Calvanese,et al.  DL-Lite: Tractable Description Logics for Ontologies , 2005, AAAI.

[28]  Boris Motik,et al.  HermiT: A Highly-Efficient OWL Reasoner , 2008, OWLED.

[29]  Hirofumi Katsuno,et al.  Propositional Knowledge Base Revision and Minimal Change , 1991, Artif. Intell..

[30]  Diego Calvanese,et al.  Capturing model-based ontology evolution at the instance level: The case of DL-Lite , 2013, J. Comput. Syst. Sci..

[31]  Bernhard Nebel,et al.  Belief Revision and Default Reasoning: Syntax-Based Approaches , 1991, KR.