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Quasi-Acyclic Propositional Horn Knowledge Bases: Optimal Compression
October 1995 (vol. 7 no. 5)
pp. 751-762

Abstract—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 [16] that the minimization of Horn functions, i.e., Boolean functions associated with Horn knowledge bases, is NP-complete.

This paper deals with the minimization of quasi-acyclic Horn functions, the class of which properly includes the two practically significant classes of quadratic and of acyclic functions. A procedure is developed for recognizing 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 minimization of quasi-acyclic Horn functions.

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Index Terms:
Expert systems, propositional knowledge bases, Horn clauses, logical equivalence, Boolean functions, logic minimization, knowledge compression, acyclic rule bases.
Citation:
Peter L. Hammer, Alexander Kogan, "Quasi-Acyclic Propositional Horn Knowledge Bases: Optimal Compression," IEEE Transactions on Knowledge and Data Engineering, vol. 7, no. 5, pp. 751-762, Oct. 1995, doi:10.1109/69.469822
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