Journal of the Association for Computing Machinery, Vol. 43, No. 2, March 1996, pp. 193–224.

Knowledge Compilation and Theory Approximation

BART SELMAN

AND

HENRY KAUTZ

Abstract. Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often too restrictive for practical applications, whereas the latter leads to uncertainty about exactly what can and cannot be inferred from the knowledge base. We present a third alternative, in which knowledge given in a general representation level is translated (compiled) into a tractable form—allowing for efficient subsequent query answering.

We show how propositional logical theories can be compiled into Horn theories that approximate the original information. The approximations bound the original theory from below and above in terms of logical strength. The procedures are extended to other tractable languages (for example, binary clauses) and to the first-order case. Finally, we demonstrate the generality of our approach by compiling concept descriptions in a general frame-based language into a tractable form.

Categories and Subject Descriptors. F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic; I.2.3 [Artificial Intelligence]: Deduction and Theorem Proving; I.2.4 [Artificial Intelligence]: Knowledge Representation Formalisms and Methods

General Terms. Algorithms, Experimentation, Theory

Additional Key words and Phrases. Efficient reasoning methods, Horn clauses, knowledgebased optimization, knowledge compilation, query evaluation, theory approximations

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