Forgetting in Multi-Agent Modal Logics

In the past decades, forgetting has been investigated for many logics and has found many applications in knowledge representation and reasoning. However, forgetting in multi-agent modal logics has largely been unexplored. In this paper, we study forgetting in multi-agent modal logics. We adopt the semantic definition of existential bisimulation quantifiers as that of forgetting. We propose a syntactical way of performing forgetting based on the canonical formulas of modal logics introduced by Moss. We show that the result of forgetting a propositional atom from a satisfiable canonical formula can be computed by simply substituting the literals of the atom with>. Thus we show that Kn, Dn, Tn, K45n, KD45n and S5n are closed under forgetting, and hence have uniform interpolation.