Two-Dimensional Description Logics for Context-Based Semantic Interoperability

Description Logics (DLs) provide a clear and broadly accepted paradigm for modeling and reasoning about terminological knowledge. However, it has been often noted, that although DLs are well-suited for representing a single, global viewpoint on an application domain, they offer no formal grounding for dealing with knowledge pertaining to multiple heterogeneous viewpoints — a scenario ever more often approached in practical applications, e.g. concerned with reasoning over distributed knowledge sources on the Semantic Web. In this paper, we study a natural extension of DLs, in the style of two-dimensional modal logics, which supports declarative modeling of viewpoints as contexts, in the sense of McCarthy, and their semantic interoperability. The formalism is based on two-dimensional semantics, where one dimension represents a usual object domain and the other a (possibly infinite) domain of viewpoints, addressed by additional modal operators and a metalanguage, on the syntactic level. We systematically introduce a number of expressive fragments of the proposed logic, study their computational complexity and connections to related formalisms.

[1]  Stephan Tobies,et al.  Complexity results and practical algorithms for logics in knowledge representation , 2001, ArXiv.

[2]  Sasa Buvac.  Quantificational Logic of Context , 1996, AAAI/IAAI, Vol. 1.

[3]  Carsten Lutz,et al.  A Description Logic of Change , 2007, Description Logics.

[4]  John McCarthy,et al.  Generality in artificial intelligence , 1987, Resonance.

[5]  Carsten Lutz,et al.  E-connections of Description Logics , 2003, Description Logics.

[6]  Ramanathan V. Guha,et al.  Contexts for the Semantic Web , 2004, SEMWEB.

[7]  Franz Baader,et al.  Pushing the EL Envelope , 2005, IJCAI.

[8]  R. Guha.  Contexts: a formalization and some applications , 1992 .

[9]  Franz Baader,et al.  Pushing the EL Envelope Further , 2008, OWLED.

[10]  Luciano Serafini,et al.  Distributed Description Logics: Assimilating Information from Peer Sources , 2003, J. Data Semant..

[11]  Frank Wolter,et al.  Multi-Dimensional Description Logics , 1999, IJCAI.

[12]  Jiao Tao,et al.  Context Representation for the Semantic Web , 2010 .

[13]  Carsten Lutz,et al.  Probabilistic Description Logics for Subjective Uncertainty , 2010, KR.

[14]  Szymon Klarman,et al.  ALCALC: A Context Description Logic , 2010, JELIA.

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

[16]  D. Gabbay,et al.  Many-Dimensional Modal Logics: Theory and Applications , 2003 .

[17]  Heiner Stuckenschmidt,et al.  Reasoning with Multi-version Ontologies: A Temporal Logic Approach , 2005, SEMWEB.

[18]  Vasant Honavar,et al.  Package-Based Description Logics , 2009, Modular Ontologies.

[19]  Maarten Marx,et al.  Complexity of Products of Modal Logics , 1999, J. Log. Comput..

[20]  Rolf Nossum.  A decidable multi-modal logic of context , 2003, J. Appl. Log..

[21]  Ian A. Mason,et al.  Propositional Logic of Context , 1993, AAAI.

[22]  Carsten Lutz,et al.  Temporal Description Logics: A Survey , 2008, 2008 15th International Symposium on Temporal Representation and Reasoning.