Monotonic modal logics with a conjunction

Abstract

Monotone modal logics have emerged in several application areas such as computer science and social choice theory. Since many of the most studied selfextensional logics have a conjunction, in this paper we study some distributive extensions obtained from a semilattice based deductive system with monotonic modal operators, and we give them neighborhood and algebraic semantics. For each logic defined our main objective is to prove completeness with respect to its characteristic class of monotonic frames.