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Safety for bisimulation in monadic second-order logic

By M. Hollenberg


We characterize those formulas of MSO m(monadic second-order logic) that are safe for bisimulation: formulas defining binary relations such that any bisimulation is also a bisimulation with\ud respect to these defined relations. Every such formula is equivalent to one constructed from μ-calculus tests, atomic actions and the regular operations. The proof uses a characterization of\ud completely additive μ-calculus formulas: formulas ø(p) that distribute over arbitrary unions. It\ud turns out that complete additivity is equivalent to distributivity over countable unions.\ud For FOL (first-order logic) a similar theorem is shown (giving an alternative proof to the original of [4]). Here though distributivity over finite unions is sufficient. This enables us to show\ud that the characterization of safe FOL-formulas carries over to the setting of finite models

Topics: Wijsbegeerte
Year: 1996
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