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Fixed Point Logics and Definable Topological Properties
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SYSNO ASEP 0563276 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Fixed Point Logics and Definable Topological Properties Author(s) Fernández-Duque, David (UIVT-O) SAI, ORCID, RID
Gougeon, P. (FR)Source Title Logic, Language, Information, and Computation. - Cham : Springer, 2022 / Ciabattoni A. ; Pimentel E. ; de Queiroz R. J. G. B - ISSN 0302-9743 - ISBN 978-3-031-15297-9 Pages roč. 13468 (2022), s. 36-52 Series Lecture Notes in Computer Science Number of pages 17 s. Publication form Print - P Action WoLLIC 2022: International Workshop on Logic, Language, Information, and Computation /28./ Event date 20.09.2022 - 23.09.2022 VEvent location Iași Country RO - Romania Event type WRD Language eng - English Country CH - Switzerland Keywords Mu-calculus ; Expressivity ; Topological semantics OECD category Pure mathematics Institutional support UIVT-O - RVO:67985807 UT WOS 000866553800003 EID SCOPUS 85138821241 DOI 10.1007/978-3-031-15298-6_3 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2023
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