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Modified tableaux for some kinds of multimodal logics

Emilio Gómez-Caminero

pp. 283-294

A multimodal logic is a logic where a certain number of different modal operators appear. In some of these logics we can have at our disposal a labeled tableaux method whereby different modal operators give rise to different labels. The properties of the accessibility relations, in the semantic view, may be treated by means of what we call inheritance rules.The easiest cases are those in which all modal operators are of the same type, such as multiagent epistemic or doxastic logic. In these cases we can propose a modular tableau method that we can adapt to the most important systems only changing the inheritance rules. Although some of these systems give rise to infinite branches, we can avoid the infinity by means of some restrictions in the use of rules. More complicated cases require additional rules to deal with the relationship between different modal operators. Finally, some infinitary operators, such as common knowledge or sometime, may be dealt with using DB-tableaux or recursive rules.

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Full citation:

Gómez-Caminero, E. (2016)., Modified tableaux for some kinds of multimodal logics, in J. Redmond, O. Martins & . Fernández (eds.), Epistemology, knowledge and the impact of interaction, Dordrecht, Springer, pp. 283-294.

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