Mixed Integer Programming, General Concept Inclusions and Fuzzy Description Logics

Fuzzy Description Logics (fuzzy DLs) have been proposed as a language to describe structured knowledge with vague concepts. In [19], a solution based on Mixed Integer Linear Programming has been proposed to deal with fuzzy DLs under Lukasiewicz semantics in which typical membership functions, such as triangular and trapezoidal functions, can be explicitly represented in the language. A major theoretical and computational limitation so far is the inability to deal with General Concept Inclusions (GCIs), which is an important feature of classical DLs. In this paper, we address this issue and develop a calculus for fuzzy DLs with GCIs under various semantics: classical logic, \Zadeh semantics", and Lukasiewicz logic.

[1]  Yin Yang,et al.  An enhanced model for searching in semantic portals , 2005, WWW '05.

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

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

[4]  Reiner Hähnle,et al.  Advanced Many-Valued Logics , 2001 .

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

[6]  Baowen Xu,et al.  Extended Fuzzy Description Logic ALCN , 2005, KES.

[7]  Steffen Hölldobler,et al.  The Fuzzy Description Logic ALCFH with Hedge Algebras as Concept Modifiers , 2003, J. Adv. Comput. Intell. Intell. Informatics.

[8]  Jeff Z. Pan,et al.  A Fuzzy Description Logic for Multimedia Knowledge Representation , 2005 .

[9]  Ian Horrocks,et al.  Reasoning with Individuals for the Description Logic SHIQ , 2000, CADE.

[10]  Martin Otto,et al.  Back and forth between guarded and modal logics , 2002, TOCL.

[11]  Umberto Straccia,et al.  Uncertainty and description logic programs over lattices , 2006, Fuzzy Logic and the Semantic Web.

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

[13]  Thomas Lukasiewicz,et al.  An Overview of Uncertainty and Vagueness in Description Logics for the Semantic Web an Overview of Uncertainty and Vagueness in Description Logics for the Semantic Web , 2006 .

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

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

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

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

[18]  Via S. Maria.  A Framework for the Retrieval of Multimedia Objects Based on Four-Valued Fuzzy Description Logics , 1999 .

[19]  Umberto Straccia,et al.  Towards a Fuzzy Description Logic for the Semantic Web (Preliminary Report) , 2005, ESWC.

[20]  Harvey M. Salkin,et al.  Foundations of integer programming , 1989 .

[21]  Nguyen Hoang Nga,et al.  The Subsumption Problem of the Fuzzy Description Logic ALCFH , 2004 .

[22]  Ian Horrocks,et al.  Practical Reasoning for Very Expressive Description Logics , 2000, Log. J. IGPL.

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

[24]  Carsten Lutz,et al.  Description Logics with Concrete Domains-A Survey , 2002, Advances in Modal Logic.

[25]  Ian Horrocks,et al.  The Fuzzy Description Logic f-SHIN , 2005, ISWC-URSW.

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

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

[28]  Fuzzy Description Logics with Concrete Domains , 2005 .

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

[30]  Nguyen Hoang Nga,et al.  THE FUZZY DESCRIPTION LOGIC ALCFLH , 2005 .

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

[32]  Daniel Sánchez,et al.  Fuzzy quantification in fuzzy description logics , 2006, Fuzzy Logic and the Semantic Web.

[33]  Piero A. Bonatti,et al.  Some Complexity Results on Fuzzy Description Logics , 2003, WILF.