Anti-prenexing and Prenexing for Modal Logics

Efficient proof methods for normal modal logics are highly desirable, as such logical systems have been widely used in computer science to represent complex situations. Resolution-based methods are often designed to deal with formulae in a normal form and the efficiency of the method (also) relies on how efficient (in the sense of producing fewer and/or shorter clauses) the translation procedure is. We present a normal form for normal modal logics and show how the use of simplification, for specific normal logics, together with anti-prenexing and prenexing techniques help us to produce better sets of clauses.