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<p><it>Abstract</it>—Horn knowledge bases are widely used in many applications. This paper is concerned with the optimal compression of propositional Horn production rule bases - one of the most important knowledge bases used in practice. The problem of knowledge compression is interpreted as a problem of Boolean function minimization. It was proved in [<ref rid="BIBK075116" type="bib">16</ref>] that the minimization of Horn functions, i.e., Boolean functions associated with Horn knowledge bases, is NP-complete.</p><p>This paper deals with the minimization of <it>quasi-acyclic</it> Horn functions, the class of which properly includes the two practically significant classes of quadratic and of acyclic functions. A procedure is developed for <it>recognizing</it> in quadratic time the quasi-acyclicity of a function given by a Horn CNF, and a graph-based algorithm is proposed for the quadratic time <it>minimization</it> of quasi-acyclic Horn functions.</p>
Expert systems, propositional knowledge bases, Horn clauses, logical equivalence, Boolean functions, logic minimization, knowledge compression, acyclic rule bases.

P. L. Hammer and A. Kogan, "Quasi-Acyclic Propositional Horn Knowledge Bases: Optimal Compression," in IEEE Transactions on Knowledge & Data Engineering, vol. 7, no. , pp. 751-762, 1995.
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