On the Relative Expressiveness of Description Logics and Predicate Logics

Abstract It is natural to view concept and role definitions in description logics as expressing monadic and dyadic predicates in predicate calculus. We show that the descriptions built using the constructors usually considered in the DL literature are characterized exactly as the predicates definable by formulas in \ tL3, the subset of first-order predicate calculus with monadic and dyadic predicates which allows only three variable symbols. In order to handle “number bounds”, we allow numeric quantifiers, and for transitive closure of roles we use infinitary disjunction. Using previous results in the literature concerning languages with limited numbers of variables, we get as corollaries the existence of formulas of FOPC which cannot be expressed as descriptions. We also show that by omitting role composition, descriptions express exactly the formulas in \ tL2, which is known to be decidable.

[1]  Franz Baader A Formal Definition for the Expressive Power of Knowledge Representation Languages , 1990, ECAI.

[2]  Werner Nutt,et al.  Subsumption between queries to object-oriented databases , 1994, Inf. Syst..

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

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

[5]  Neil Immerman,et al.  Relational Queries Computable in Polynomial Time , 1986, Inf. Control..

[6]  Phokion G. Kolaitis,et al.  On the Expressive Power of Datalog: Tools and a Case Study , 1995, J. Comput. Syst. Sci..

[7]  Alexander Borgida,et al.  Loading data into description reasoners , 1993, SIGMOD Conference.

[8]  Bill Swartout,et al.  Description-Logic Knowledge Representation System Specification from the KRSS Group of the ARPA Know , 1993 .

[9]  Johan van Benthem,et al.  Back and Forth Between Modal Logic and Classical Logic , 1995, Log. J. IGPL.

[10]  Harry R. Lewis,et al.  Unsolvable classes of quantificational formulas , 1979 .

[11]  Peter F. Patel-Schneider,et al.  Undecidability of Subsumption in NIKL , 1989, Artif. Intell..

[12]  Francesco M. Donini,et al.  A Hybrid System with Datalog and Concept Languages , 1991, AI*IA.

[13]  Uwe Mönnich,et al.  Aspects of Philosophical Logic , 1981 .

[14]  Neil Immerman Upper and lower bounds for first order expressibility , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[15]  Robert M. MacGregor,et al.  A Deductive Pattern Matcher , 1988, AAAI.

[16]  Michael Mortimer,et al.  On languages with two variables , 1975, Math. Log. Q..

[17]  Neil Immerman,et al.  An optimal lower bound on the number of variables for graph identification , 1992, Comb..

[18]  Ronald J. Brachman,et al.  A Structural Paradigm for Representing Knowledge. , 1978 .

[19]  Dov M. Gabbay,et al.  EXPRESSIVE FUNCTIONAL COMPLETENESS IN TENSE LOGIC , 1981 .

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

[21]  Werner Nutt,et al.  Terminological Knowledge Representation: A Proposal for a Terminological Logic , 1991, Description Logics.

[22]  A. Tarski,et al.  A Formalization Of Set Theory Without Variables , 1987 .