Fixed Point Logics and Definable Topological Properties

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00563276" target="_blank" >RIV/67985807:_____/22:00563276 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-031-15298-6_3" target="_blank" >http://dx.doi.org/10.1007/978-3-031-15298-6_3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-15298-6_3" target="_blank" >10.1007/978-3-031-15298-6_3</a>

Result language
angličtina
Original language name
Fixed Point Logics and Definable Topological Properties
Original language description
Modal logic enjoys topological semantics that may be traced back to McKinsey and Tarski, and the classification of topological spaces via modal axioms is a lively area of research. In the past two decades, there has been interest in extending topological modal logic to the language of the mu-calculus, but previously no class of topological spaces was known to be mu-calculus definable that was not already modally definable. In this paper we show that the full mu-calculus is indeed more expressive than standard modal logic, in the sense that there are classes of topological spaces (and weakly transitive Kripke frames) which are mu-definable, but not modally definable. The classes we exhibit satisfy a modally definable property outside of their perfect core, and thus we dub them imperfect spaces. We show that the mu-calculus is sound and complete for these classes. Our examples are minimal in the sense that they use a single instance of a greatest fixed point.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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