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Forgetting in multi-agent modal logics
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DOI：10.1016/j.artint.2018.08.003.png)
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Abstract
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In the past decades, forgetting has been investigated for many logics and has found many applications in knowledge representation and reasoning. 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 resort to canonical formulas of modal logics introduced by Moss. An arbitrary modal formula is equivalent to the disjunction of a unique set of satisfiable canonical formulas. We show that, for the logics of K-n, D-n, T-n, K45(n), KD45(n) and S5(n), the result of forgetting an atom from a satisfiable canonical formula can be computed by simply substituting the literals of the atom with T. Thus we show that these logics are closed under forgetting, and hence have uniform interpolation. Finally, we generalize the above results to include common knowledge of propositional formulas. (C) 2018 Elsevier B.V. All rights reserved.
Keywords:
Multi-agent modal logics
Forgetting
Uniform interpolation
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