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On the complexity of the instance checking problem in concept languages with existential quantification

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Abstract

Most of the work regarding complexity results for concept languages consider subsumption as the prototypical inference. However, when concept languages are used for building knowledge bases including assertions on individuals, the basic deductive service of the knowledge base is the so-called instance checking, which is the problem of checking if an individual is an instance of a given concept. We consider a particular concept language, calledALE, and we address the question of whether instance checking can be really solved by means of subsumption algorithms in this language. Therefore, we indirectly ask whether considering subsumption as the prototypical inference is justified. Our analysis, carried out considering two different measure of complexity, shows that inALE instance checking is strictly harder than subsumption. This result singles out a new source of complexity in concept languages, which does not show up when checking subsumption between concepts.

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References

  • Baader, F. & Hollunder, B. (1991). A Terminological Knowledge Representation System with Complete Inference Algorithm. InProc. Workshop on Processing Declarative Knowledge, PDK-19. Lecture Notes in Artificial Intelligence. Springer-Verlag: New York.

    Google Scholar 

  • Brachman, R.J. & Levesque, H.J. (1984). The Tractability of Subsumption in Frame-Based Description Languages. InProc. 4th Nat. Conf. on Artificial Intelligence AAAI-84.

  • Donini, F.M., Hollunder, B., Lenzerini, M., Marchetti Spaccamela, A., Nardi, D. & Nutt, W.. (1992a). The Complexity of Existential Quantification in Concept Languages,Artificial Intelligence, 2–3, 309–327.

    Google Scholar 

  • Donini, F.M., Lenzerini, M., Nardi, D. & Nutt, W. (1991). The Complexity of Concept Languages. In James Allen, Richard Fikes, and Erik Sandewall (Eds.),Proc. 2nd Int. Conf. on Principles of Knowledge Representation and Reasoning KR-91, pages 151–162, Morgan Kaufmann.

  • Donini, F.M., Lenzerini, M., Nardi, D., Nutt, W. & Schaerf, A. (1992b). Adding Epistemic Operators to Concept Languages. InProc. 3rd Int. Conf. On Principles of Knowledge Representation and Reasoning KR-92, pages 342–353.

  • Donini, F.M., Lenzerini, M., Nardi, D. & Schaerf, A. (1992c). From Subsumption to Instance Checking, Technical Report 15.92, Dipartimento di Informatica e Sistemistica, Universita di Roma “La Sapienza.”

  • Garey, M.R. & Johnson, D.S. (1979).Computers and Intractability—A guide to NP-completeness, Freeman: San Francisco.

    Google Scholar 

  • Lenzerini, M. & Schaerf, A. (1991a). Concept Languages as Query Languages. InProc. 9th Nat. Conf. on Artificial Intelligence AAAI-91.

  • Lenzerini, M. & Schaerf, A. (1991b). Querying Concept-Based Knowledge Bases. InProc. Workshop on Processing Declarative Knowledge, PDK-91, Lecture Notes in Artificial Intelligence. Springer-Verlag: New York.

    Google Scholar 

  • Levesque, H.J. & Brachman, R.J. (1987). Expressiveness and Tractability in Knowledge Representation and Reasoning,Computational Intelligence, 3, 78–93.

    Google Scholar 

  • MacGregor, R. (1991). Inside the LOOM Description Classifier,SIGART Bulletin, 2(3); 88–92.

    Google Scholar 

  • Nebel, B. (1988). Computational Complexity of Terminological Reasoning in BAck,Artificial Intelligence, 34(3), 371–383.

    Google Scholar 

  • Nebel, B. (1990a)Reasoning and Revision in Hybrid Representation Systems, Lecture Notes in Artificial Intelligence. Springer-Verlag: New York.

    Google Scholar 

  • Nebel, B. (1990b). Terminological Reasoning is Inherently Intractable.Artificial Intelligence, 43, 235–249.

    Google Scholar 

  • Nebel, B. (1991). Terminological Cycles: Semantics and Computational Properties. In John F. Sowa (ed.),Principles of Semantic Networks, pages 331–361. Morgan Kaufmann.

  • Patel-Schneider, P.F., McGuiness, D.L., Brachman, R.J., Alperin Resnick, L. & Borgida, A. (1991). The Classic Knowledge Representation System: Guiding Principles and Implementation Rationale.SIGART Bulletin, 2(3); 108–113.

    Google Scholar 

  • Peltason, C. (1991). The BACK System-An Overview,SIGART Bulletin, 2(3); 114–119.

    Google Scholar 

  • Schmidt-Schauβ, M. (1989). Subsumption in KL-ONE Is Undecidable. In Ron J. Brachman, Hector J. Levesque, and Ray Reiter Ed,Proc. 1st Int. Conf. on Principles of Knowledge Representation and Reasoning KR-89. Morgan Kaufmann.

  • Schmidt-Schauβ, M. & Smolka, G. (1991). Attributive Concept Descriptions with Complements,Artificial Intelligence, 48(1), 1–26.

    Google Scholar 

  • Vardi, M. (1982). The Complexity of Relational Query Languages.In14th ACM Symp. on Theory of Computing, pages 137–146.

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Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica Università di Roma “la Sapienza”, Via Salaria 113, 00198, Roma, Italia

    Andrea Schaerf

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  1. Andrea Schaerf
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This work has been supported by the ESPRIT Basic Research Action N.6810-COMPULOG 2 and by the Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo of the CNR (Italian Research Council).

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Schaerf, A. On the complexity of the instance checking problem in concept languages with existential quantification. J Intell Inf Syst 2, 265–278 (1993). https://doi.org/10.1007/BF00962071

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