Bisimulations and Boolean Vectors

A modal accessibility relation is just a transition relation, and so can be represented by a {0, 1} valued transition matrix. Starting from this observation, I first show that the machinery of matrices, over Boolean algebras more general than the two-valued one, is appropriate for investigating multi-modal semantics. Then I show that bisimulations have a rather elegant theory, when expressed in terms of transformations on Boolean vector spaces. The resulting theory is a curious hybrid, fitting between conventional modal semantics and conventional linear algebra. I don’t know where the investigations begun here will ultimately wind up, but in the meantime the approach has a kind of curious charm that others may find appealing.
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Lars Hansen (2005). On an Algebra of Lattice-Valued Logic. Journal of Symbolic Logic 70 (1):282 - 318.

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