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

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.

[1]  Bernhard Nebel,et al.  Reasoning and Revision in Hybrid Representation Systems , 1990, Lecture Notes in Computer Science.

[2]  Hector J. Levesque,et al.  Expressiveness and tractability in knowledge representation and reasoning 1 , 1987, Comput. Intell..

[3]  Bernhard Nebel,et al.  Terminological Reasoning is Inherently Intractable , 1990, Artif. Intell..

[4]  Peter F. Patel-Schneider,et al.  The CLASSIC knowledge representation system: guiding principles and implementation rationale , 1991, SGAR.

[5]  Franz Baader,et al.  A Terminological Knowledge Representation System with Complete Inference Algorithms , 1991, PDK.

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

[7]  Moshe Y. Vardi.  The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

[8]  Projektgruppe WINOPostfa.  A Terminological Knowledge Representation System with Complete Inference Algorithms , 1991 .

[9]  Maurizio Lenzerini,et al.  Querying Concept-based Knowledge Bases , 1991, PDK.

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

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

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

[13]  Christof Peltason.  The BACK system—an overview , 1991, SGAR.

[14]  Hector J. Levesque,et al.  The Tractability of Subsumption in Frame-Based Description Languages , 1984, AAAI.

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

[16]  Werner Nutt,et al.  The Complexity of Existential Quantification in Concept Languages , 1992, Artif. Intell..

[17]  Robert M. MacGregor,et al.  Inside the LOOM description classifier , 1991, SGAR.

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

[19]  Werner Nutt,et al.  Adding Epistemic Operators to Concept Languages , 1992, KR.

[20]  Maurizio Lenzerini,et al.  Concept Languages as Query Languages , 1991, AAAI.