Essential and redundant rules in Horn knowledge bases

A production rule of a knowledge base ia called Ed sential if it is present in any prime knowledge ba8e which is logically equivalent to the given one. The identification of essential rules indicates the degree of fkeedom we have in constructing logically equivalent transfomaationa of the base, by specifying the set of rules which must remain in place, and implicitly showing which rulea could be replaced by other oned. A prime rule is called redundant if it is not present in any irredundant prime knowledge base which ia logically equivalent to the given one. The recognition of redundancy of a particular pn’me rule in a knowledge base will eliminate such rule from consideration in any future simplificationa of the knowledge base. This paper provides combinatorial characterizationa and computational recognition procedures of essentiality and redundancy of prime rules of Horn knowledge bases.