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_____%2F24%3A00580737" target="_blank" >RIV/67985807:_____/24:00580737 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1017/S0960129523000385" target="_blank" >https://doi.org/10.1017/S0960129523000385</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S0960129523000385" target="_blank" >10.1017/S0960129523000385</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, and we show that least fixed points alone do not suffice to define any class of spaces that is not already modally definable.

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, and we show that least fixed points alone do not suffice to define any class of spaces that is not already modally definable.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematical Structures in Computer Science

ISSN

0960-1295

e-ISSN

1469-8072

Svazek periodika

34

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

17

Strana od-do

81-97

Kód UT WoS článku

001124258200001

EID výsledku v databázi Scopus

2-s2.0-85179984864