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 T. Thus we show that Kn, Dn, Tn, K45n, KD45n and S5n are closed under forgetting, and hence have uniform interpolation.
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Forgetting in Multi-Agent Modal Logics
Semantic Scholar · Computer Science · 2016
Abstract
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 T. Thus we show that Kn, Dn, Tn, K45n, KD45n and S5n are closed under forgetting, and hence have uniform interpolation.