On the Complexity of the Maximum Satisfiability Problem for Horn Formulas

or equivalently, as I-Iom formulas. As many authors have pointed out (see, e.g., [S]), Horn formulas naturally arise in logic databases; actually, they are used to formulate queries and to express integrity constraints. As the size of databases and knowledge bases grows, it becomes more and more crucial to check their consistency and, if not, to determine the maximum number of relations that can be satisfied. In the domain of propositional calculus, this problem corresponds to the maximum satisfiability problem for Morn formulas. In the present article, we prove the IW-completeness of this problem even under strong restrictions on the I-Iom formulas. On the we show that there exists a polynomial-time algorithm for the corresponding Maximum Satisfiability Problem.