Disjunctive and conjunctive representations in finite lattices and convexity spaces

摘要

The concepts of disjunctive and conjunctive form, implicants and implicata, well known in lattices of Boolean functions, are examined in the general context of finite lattices and finite convexity spaces. The validity of the Blake-Quince consensus procedure for the determination of the prime implicants is shown to depend on a simple form of join reducibility. In the context of conceity spaces, another algebraic procedure for the determination of the prime implicants, based on distributivity, is seen to be contingent on the Helly property for convex sets.