On weak positive predicates over a finite set

Predicates that are preserved by a semi-lattice function are considered. These predicates are called weak positive. A representation of these predicates are proposed in the form of generalized conjunctive normal forms (GCNFs). Properties of GCNFs of these predicates are obtained. Based on the properties obtained, more efficient polynomial-time algorithms are proposed for solving the generalized satisfiability problem in the case when all initial predicates are preserved by a certain semi-lattice function.