Reasoning within expressive fuzzy rough description logics

Abstract It is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are suitable, well-known logics for managing structured knowledge that have gained considerable attention the last decade. The current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in DLs are analyzed in this paper. An integration between the theories of fuzzy DLs and rough DLs has been attempted by providing fuzzy rough DLs based on fuzzy rough set theory. The syntax, semantics and properties of fuzzy rough DLs are given. It is proved that the satisfiability, subsumption, entailment and ABox consistency reasoning in fuzzy rough DLs may be reduced to the ABox consistency reasoning in the corresponding fuzzy DLs.

[1]  Petr Hájek,et al.  Making fuzzy description logic more general , 2005, Fuzzy Sets Syst..

[2]  G. Stamou,et al.  Reasoning with Very Expressive Fuzzy Description Logics , 2007, J. Artif. Intell. Res..

[3]  Bernhard Hollunder.  An alternative proof method for possibilistic logic and its application to terminological logics , 1994, Int. J. Approx. Reason..

[4]  Wojciech Ziarko,et al.  Probabilistic approach to rough sets , 2008, Int. J. Approx. Reason..

[5]  John Yen,et al.  Generalizing Term Subsumption Languages to Fuzzy Logic , 1991, IJCAI.

[6]  Steffen Staab,et al.  Handbook on Ontologies (International Handbooks on Information Systems) , 2004 .

[7]  Ian Horrocks,et al.  Keys, Nominals, and Concrete Domains , 2003, IJCAI.

[8]  Tong-Jun Li,et al.  Rough approximation operators on two universes of discourse and their fuzzy extensions , 2008, Fuzzy Sets Syst..

[9]  Dimiter Vakarelov,et al.  Information , 1989, British Journal of Music Education.

[10]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[11]  Wen-Xiu Zhang,et al.  Measuring roughness of generalized rough sets induced by a covering , 2007, Fuzzy Sets Syst..

[12]  Gert Smolka,et al.  Attributive Concept Descriptions with Complements , 1991, Artif. Intell..

[13]  Wei-Zhi Wu,et al.  Generalized fuzzy rough sets , 2003, Inf. Sci..

[14]  Shi Zhongzhi,et al.  A logical foundation for the semantic Web , 2005 .

[15]  Guilong Liu,et al.  Generalized rough sets over fuzzy lattices , 2008, Inf. Sci..

[16]  Chris Cornelis,et al.  Fuzzy Rough Sets: The Forgotten Step , 2007, IEEE Transactions on Fuzzy Systems.

[17]  Ian Horrocks,et al.  A Description Logic with Transitive and Inverse Roles and Role Hierarchies , 1999, J. Log. Comput..

[18]  Umberto Straccia,et al.  A fuzzy description logic for the semantic web , 2006, Fuzzy Logic and the Semantic Web.

[19]  Qingguo Li,et al.  Construction of rough approximations in fuzzy setting , 2007, Fuzzy Sets Syst..

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

[21]  Van-Nam Huynh,et al.  A roughness measure for fuzzy sets , 2005, Inf. Sci..

[22]  Umberto Straccia,et al.  Description Logics over Lattices , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[23]  Fernando Bobillo,et al.  Optimizing the Crisp Representation of the Fuzzy Description Logic SROIQ , 2007, URSW.

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

[25]  Degang Chen,et al.  Measures of general fuzzy rough sets on a probabilistic space , 2008, Inf. Sci..

[26]  M. de Rijke,et al.  JFAK. Essays Dedicated to Johan van Benthem on the occasion of his 50th Birthday , 1999 .

[27]  Fernando Bobillo,et al.  DeLorean: A Reasoner for Fuzzy OWL 1.1 , 2008, URSW.

[28]  Siu Cheung Hui,et al.  Automatic fuzzy ontology generation for semantic Web , 2006, IEEE Transactions on Knowledge and Data Engineering.

[29]  R. Słowiński.  Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory , 1992 .

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

[31]  Yiyu Yao,et al.  Probabilistic rough set approximations , 2008, Int. J. Approx. Reason..

[32]  Baowen Xu,et al.  Discrete Tableau Algorithms for FSHI , 2006, Description Logics.

[33]  Daowu Pei,et al.  A generalized model of fuzzy rough sets , 2005, Int. J. Gen. Syst..

[34]  Werner Nutt,et al.  Basic Description Logics , 2003, Description Logic Handbook.

[35]  Xu Baowen,et al.  On Computational Complexity of the Extended Fuzzy Description Logic with Numerical Restriction , 2006 .

[36]  Umberto Straccia,et al.  Description Logics with Fuzzy Concrete Domains , 2005, UAI.

[37]  Bernhard Nebel,et al.  Terminological Reasoning is Inherently Intractable , 1990, Artif. Intell..

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

[39]  Jianfeng Du,et al.  Extending description logics with uncertainty reasoning in possibilistic logic , 2007, Int. J. Intell. Syst..

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

[41]  Patrick Doherty,et al.  Towards a Framework for Approximate Ontologies , 2003, Fundam. Informaticae.

[42]  Xizhao Wang,et al.  On the generalization of fuzzy rough sets , 2005, IEEE Transactions on Fuzzy Systems.

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

[44]  Ian Horrocks,et al.  Decidability of SHIQ with Complex Role Inclusion Axioms , 2003, IJCAI.

[45]  Radko Mesiar,et al.  Triangular norms. Position paper I: basic analytical and algebraic properties , 2004, Fuzzy Sets Syst..

[46]  Umberto Straccia,et al.  General Concept Inclusions inFluzzy Description Logics , 2006, ECAI.

[47]  Sankar K. Pal,et al.  Roughness of a Fuzzy Set , 1996, Inf. Sci..

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

[49]  J. Goguen.  L-fuzzy sets , 1967 .

[50]  Umberto Straccia,et al.  fuzzyDL: An expressive fuzzy description logic reasoner , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[51]  Umberto Straccia,et al.  Fuzzy description logics under Gödel semantics , 2009, Int. J. Approx. Reason..

[52]  Qiang Shen,et al.  Fuzzy-Rough Sets Assisted Attribute Selection , 2007, IEEE Transactions on Fuzzy Systems.

[53]  Carsten Lutz,et al.  NEXP TIME-complete description logics with concrete domains , 2004, TOCL.

[54]  Fabio Grandi,et al.  On Expressive Number Restrictions in Description Logics , 2001, Description Logics.

[55]  Franz Baader.  Augmenting Concept Languages by Transitive Closure of Roles: An Alternative to Terminological Cycles , 1991, IJCAI.

[56]  Manfred Jaeger,et al.  Probabilistic Reasoning in Terminological Logics , 1994, KR.

[57]  Suqin Tang,et al.  Reasoning with rough description logics: An approximate concepts approach , 2008, Information Sciences.

[58]  Ewa Orlowska,et al.  Kripke semantics for knowledge representation logics , 1990, Stud Logica.

[59]  Didier Dubois,et al.  Putting Rough Sets and Fuzzy Sets Together , 1992, Intelligent Decision Support.

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

[61]  Piero A. Bonatti,et al.  On the undecidability of logics with converse, nominals, recursion and counting , 2004, Artif. Intell..

[62]  Diego Calvanese,et al.  Reasoning on UML class diagrams , 2005, Artif. Intell..

[63]  Ian Horrocks,et al.  The Even More Irresistible SROIQ , 2006, KR.

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

[65]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[66]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[67]  Ian Horrocks,et al.  From SHIQ and RDF to OWL: the making of a Web Ontology Language , 2003, J. Web Semant..

[68]  Christian Eitzinger,et al.  Triangular Norms , 2001, Künstliche Intell..

[69]  Michel C. A. Klein,et al.  Description Logics with Approximate Definitions - Precise Modeling of Vague Concepts , 2007, IJCAI.

[70]  SHIZhongzhi,et al.  A logical foundation for the semantic Web , 2005 .

[71]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[72]  Jiang Yun-cheng,et al.  Fuzzy Description Logic for Semantics Representation of the Semantic Web , 2007 .