Combinatorial Problems for Horn Clauses

摘要

Given a family of Horn clauses, what is the minimal number of Horn clauses implying all other clauses in the family? What is the maximal number of Horn clauses from the family without having resolvents of a certain kind? We consider various problems of this type, and give some sharp bounds. We also consider the probability that a random family of a given size implies all other clauses in the family, and we prove the existence of a sharp threshold.