On Triangular Norm Based Fuzzy Description Logics

Description Logics (DLs) are knowledge representa- tion languages useful to represent concepts and roles. Fuzzy De- scription Logics (FDLs) incorporate both vague concepts and vague roles modeling them as fuzzy sets and fuzzy relations respectively. In the present paper, following ideas from Hajek, we propose the use of t-norm based (fuzzy) logics with truth constants in the language as logics underlying the fuzzy description language. We introduce the languages ALCL∗(S) and ALCL∗(S) as an adequate syntactical counterpart of some semantic calculi given in different works dealing with FDLs.

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

[2]  L. A. Zadeh,et al.  Fuzzy logic and approximate reasoning , 1975, Synthese.

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

[4]  Petr Hájek.  What does mathematical fuzzy logic offer to description logic? , 2006, Fuzzy Logic and the Semantic Web.

[5]  Christopher Tresp,et al.  A Description Logic for Vague Knowledge , 1998, ECAI.

[6]  E. Trillas,et al.  in Fuzzy Logic , 2002 .

[7]  Umberto Straccia.  Fuzzy ALC with Fuzzy Concrete Domains , 2005 .

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

[9]  Lluis Godo,et al.  Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results , 2007, Fuzzy Sets Syst..

[10]  Günter Asser,et al.  Zeitschrift für mathematische Logik und Grundlagen der Mathematik , 1955 .

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

[12]  Franco Montagna,et al.  Equational Characterization of the Subvarieties of BL Generated by t-norm Algebras , 2004, Stud Logica.

[13]  Umberto Straccia,et al.  Mixed Integer Programming, General Concept Inclusions and Fuzzy Description Logics , 2007, EUSFLAT Conf..

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

[15]  L. Godo,et al.  On Completeness Results for Predicate Lukasiewicz, Product, Godel and Nilpotent Minimum Logics Expanded with Truth-constants , 2007 .

[16]  Petr Hájek,et al.  Residuated fuzzy logics with an involutive negation , 2000, Arch. Math. Log..

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

[18]  A. Monteiro.  Sur les algèbres de Heyting symétriques , 1980 .

[19]  Lluis Godo,et al.  Basic Fuzzy Logic is the logic of continuous t-norms and their residua , 2000, Soft Comput..

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