TBox and ABox Reasoning in Expressive Description Logics

A Description Logic (DL) system is characterized by four fundamental aspects: the set of constructs used in concept and role expressions, the kind of assertions allowed in the TBox (assertions on concepts) and the ABox (assertions on individuals), and the inference mechanisms for reasoning on both the TBox and the ABox. Most of the research done in the last decade made several simplifying assumptions on the above aspects. However, the recent interest in DLs exhibited in many application areas (databases, software engineering, intelligent access to the network, planning, etc.) calls for investigating DL systems with full capabilities. The work presented in this paper represents a step in this direction. We present a sound, complete, and terminating (in worst-case EXPTIME) inference procedure that solves the problem of reasoning in a DL system with the following characteristics: it comes equipped with a very expressive language, it allows the most general form of TBox assertions, and it takes into account instance assertions on both concepts and roles in the ABox.

[1]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[2]  Amit P. Sheth,et al.  On Automatic Reasoning for Schema Integration , 1993, Int. J. Cooperative Inf. Syst..

[3]  Francesco M. Donini,et al.  Decidable Reasoning in Terminological Knowledge Representation Systems , 1993, IJCAI.

[4]  Diego Calvanese,et al.  Structured Objects: Modeling and Reasoning , 1995, DOOD.

[5]  Jon Doyle,et al.  Two Theses of Knowledge Representation: Language Restrictions, Taxonomic Classification, and the Utility of Representation Services , 1991, Artif. Intell..

[6]  Werner Nutt,et al.  The Complexity of Concept Languages , 1997, KR.

[7]  Werner Nutt,et al.  Tractable Concept Languages , 1991, IJCAI.

[8]  Jan van Leeuwen,et al.  Handbook of Theoretical Computer Science, Vol. B: Formal Models and Semantics , 1994 .

[9]  Jerzy Tiuryn,et al.  Logics of Programs , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[10]  Peter F. Patel-Schneider,et al.  A Four-Valued Semantics for Terminological Logics , 1989, Artif. Intell..

[11]  Alexander Borgida,et al.  Description Logics in Data Management , 1995, IEEE Trans. Knowl. Data Eng..

[12]  Bernhard Nebel,et al.  Terminological Cycles: Semantics and Computational Properties , 1991, Principles of Semantic Networks.

[13]  Peter F. Patel-Schneider,et al.  A Semantics and Complete Algorithm for Subsumption in the CLASSIC Description Logic , 1993, J. Artif. Intell. Res..

[14]  Bernhard Nebel,et al.  Computational Complexity of Terminological Reasoning in BACK , 1988, Artif. Intell..

[15]  Sonia Bergamaschi,et al.  On taxonomic reasoning in conceptual design , 1992, TODS.

[16]  Maurizio Lenzerini,et al.  Concept Language with Number Restrictions and Fixpoints, and its Relationship with Mu-calculus , 1994, ECAI.

[17]  Giuseppe De Giacomo.  Eliminating “converse” from converse PDL , 1996, J. Log. Lang. Inf..

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

[19]  James G. Schmolze,et al.  The KL-ONE family , 1992 .

[20]  Maurizio Lenzerini,et al.  Boosting the Correspondence between Description Logics and Propositional Dynamic Logics , 1994, AAAI.

[21]  Francesco M. Donini,et al.  Reasoning in description logics , 1997 .

[22]  Joann J. Ordille,et al.  Query-Answering Algorithms for Information Agents , 1996, AAAI/IAAI, Vol. 1.

[23]  Arantza Illarramendi,et al.  Building a Federated Relational Database System: An Approach Using a Knowledge-Based System , 1994, Int. J. Cooperative Inf. Syst..

[24]  Bernhard Nebel,et al.  An Empirical Analysis of Optimization Techniques for Terminological Representation Systems, or Making KRIS Get a Move On , 1992, KR.

[25]  Premkumar T. Devanbu,et al.  LaSSIE: a knowledge-based software information system , 1990, [1990] Proceedings. 12th International Conference on Software Engineering.

[26]  Manfred Schmidt-Schaubß,et al.  Subsumption in KL-ONE is undecidable , 1989, KR 1989.

[27]  Enrico Franconi,et al.  A Computational Account for a Description Logic of Time and Action , 1994, KR.

[28]  Maurizio Lenzerini,et al.  Representing and Using Interschema Knowledge in Cooperative Information Systems , 1993, Int. J. Cooperative Inf. Syst..

[29]  Francesco M. Donini,et al.  Deduction in Concept Languages: From Subsumption to Instance Checking , 1994, J. Log. Comput..

[30]  Andrea Schaerf.  Reasoning with Individuals in Concept Languages , 1993, AI*IA.

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

[32]  Klaus Schild,et al.  A Correspondence Theory for Terminological Logics: Preliminary Report , 1991, IJCAI.

[33]  Maurizio Lenzerini,et al.  What's in an Aggregate: Foundations for Description Logics with Tuples and Sets , 1995, IJCAI.

[34]  Diane J. Litman,et al.  Terminological Reasoning with Constraint Networks and an Application to Plan Recognition , 1992, KR.

[35]  Klaus Schild,et al.  Terminological Cycles and the Propositional µ-Calculus , 1994, KR.