In the context of extracting concepts (which are maximal item sets) and association rules from a binary data base, the graph-theoretic notion of domination was recently used to characterize the neighborhood of a concept in the corresponding lattice. In this paper, we show that the notion of domination can in fact be extended to any closure operator on a finite universe. This generalization enables us to endow notions related to Formal Concept Analysis with a logical interpretation into a set of Horn clauses. Our results also enable us to present a prospective algorithmic process which uses only local information inherited by a concept from its direct predecessors to generate rules, instead of repeatedly using all previously defined rules. This algorithm, which is very promising in practical applications, as it can be implemented to run quickly, can also be applied in the general case.