Tangled modal logic for topological dynamics
نویسندگان
چکیده
منابع مشابه
Tangled modal logic for topological dynamics
The system S4C combines topological and temporal modalities to reason about dynamical systems. Here we consider enriching its language by generalizing the use of the topological operator to its polyadic ‘tangled’ interpretation, originally introduced by Dawar and Otto in a different context. We provide an axiomatization for the extended system and show that it is sound and complete. It uses a v...
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We consider an extension of the propositional modal logic S4 which allows ♦ to act not only on isolated formulas, but also on sets of formulas. The interpretation of ♦Γ is then given by the tangled closure of the valuations of formulas in Γ, which over finite transitive, reflexive models indicates the existence of a cluster satisfying Γ. This extension has been shown to be more expressive than ...
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There has been renewed interest in recent years in McKinsey and Tarski’s interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the modal mu-calculus and to a logic of tangled closure operators that was developed by Fernández-Duque after these two languages had been shown by Dawar and Ot...
متن کاملSpatial logic of modal mu-calculus and tangled closure operators
There has been renewed interest in recent years in McKinsey and Tarski’s interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the modal mu-calculus and to a logic of tangled closure operators that was developed by Fernández-Duque after these two languages had been shown by Dawar and Ot...
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As McKinsey and Tarski [19] showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. The topological interpretation was extended by Awodey and Kishida [3] in a natural ...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2012
ISSN: 0168-0072
DOI: 10.1016/j.apal.2011.12.018