Fixed Point Logics and Definable Topological Properties

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Fixed Point Logics and Definable Topological Properties

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Fixed Point Logics and Definable Topological Properties

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Logic, Language, Information, and Computation

ISBN

978-3-031-15297-9

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

17

Strana od-do

"Roč. 13468 (2022)"

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Iași

Datum konání akce

20. 9. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000866553800003