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. In this paper, we study forgetting in multi-agent modal logics. We adopt the semantic definition of existential bisimulation quantifiers as that of forgett...

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Bibliographic Details
Published in:Artificial intelligence 2019-01, Vol.266, p.51-80
Main Authors: Fang, Liangda, Liu, Yongmei, van Ditmarsch, Hans
Format: Article
Language:English
Subjects:
Computer Science
Forgetting
Interpolation
Knowledge representation
Multi-agent modal logics
Multiagent systems
Uniform interpolation
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Summary: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 Kn, Dn, Tn, K45n, KD45n and S5n, the result of forgetting an atom from a satisfiable canonical formula can be computed by simply substituting the literals of the atom with ⊤. 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.
ISSN:0004-3702
1872-7921
DOI:10.1016/j.artint.2018.08.003