# Bisimulation invariance for monadic second-order logicsYde Venema (University of Amsterdam)

156

Old Arts

Parkville 3010

Australia

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Yde Venema (ILLC) will present "Bisimulation invariance for monadic second-order logics" on Friday, 9 February at 11 in Old Arts 156.

Abstract: of modal logics as a language for describing Kripke structures is compared to that of more classical languages such as first-order logic. An important notion in this theory is that of a bisimulation between two models. In many applications, it is natural to identify bisimilar states (i.e., states that are linked by some bisimulation), and so properties of states that are not invariant under bisimulations are irrrelevant. In this context, results that identify the bisimulation invariant fragment of some yardstick logic can be read as expressive completeness results: If M is the bisimulation-invariant fragment of L:

M = L/~,

then M is strong enough to express all relevant properties of L.

The first result of this kind was van Benthem's Characterisation Theorem that identifies basic modal logic as the bisimulation-invariant fragment of first-order logic. His result was strengthened to monadic second-order logic by Janin & Walukiewicz, who characterised the modal mu-calculus, basic modal logic extended with fixpoint operators, as its bisimulation-invariant fragment.

In the talk we discuss three variants of the Janin-Walukiewicz theorem, where in the equation L = M/~, we consider the cases where L is weak second-order logic, and where M is respectively the alternation-free fragment of the modal mu-calculus, and propositional dynamic logic (PDL).

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