Computing Extensions of Terminological Default Theories

We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of first-order logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are only applied to individuals that are explicitly present in the knowledge base. In this semantics it is possible to compute all extensions of a finite terminological default theory, which means that this type of default reasoning is decidable.

[1]  Peter F. Patel-Schneider,et al.  Living wiht Classic: When and How to Use a KL-ONE-Like Language , 1991, Principles of Semantic Networks.

[2]  Franz Baader,et al.  How to Prefer More Specific Defaults in Terminological Default Logic , 1993, IJCAI.

[3]  Camilla Schwind,et al.  A Tableau-Based Characterisation for Default Logic , 1991, ECSQARU.

[4]  Ronald J. Brachman,et al.  "I Lied About the Trees", Or, Defaults and Definitions in Knowledge Representation , 1985, AI Mag..

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

[6]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[7]  Raymond Reiter,et al.  A Theory of Diagnosis from First Principles , 1986, Artif. Intell..

[8]  Franz Baader,et al.  A Scheme for Integrating Concrete Domains into Concept Languages , 1991, IJCAI.

[9]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[10]  Kurt Konolige,et al.  Computing the Extensions of Autoepistemic and Default Logics with a Truth Maintenance System , 1990, AAAI.

[11]  Jon Doyle,et al.  A Truth Maintenance System , 1979, Artif. Intell..

[12]  Ron Rymon,et al.  Search through Systematic Set Enumeration , 1992, KR.

[13]  Drew McDermott,et al.  Non-Monotonic Logic I , 1987, Artif. Intell..

[14]  Karl Schlechta,et al.  A Semantics for Open Normal Defaults via a Modified Preferential Approach , 1993, ECSQARU.

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

[16]  Ronald J. Brachman,et al.  An overview of the KL-ONE Knowledge Representation System , 1985 .

[17]  Bernhard Hollunder.  Hybrid Inferences in KL-ONE-Based Knowledge Representation Systems , 1990, GWAI.