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Taming the 'Elsewhere': On Expressivity of Topological Languages
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SYSNO ASEP 0558050 Document Type J - Journal Article R&D Document Type The record was not marked in the RIV Subsidiary J Článek ve WOS Title Taming the 'Elsewhere': On Expressivity of Topological Languages Author(s) Fernández-Duque, David (UIVT-O) SAI, ORCID, RID Number of authors 1 Source Title Review of Symbolic Logic. - : Cambridge University Press - ISSN 1755-0203
Online 28 March 2022 (2024)Number of pages 10 s. Language eng - English Country GB - United Kingdom Keywords modal logic ; topological semantics ; expressivity OECD category Pure mathematics Method of publishing Limited access Institutional support UIVT-O - RVO:67985807 UT WOS 000780877900001 DOI 10.1017/S1755020322000120 Annotation In topological modal logic, it is well known that the Cantor derivative is more expressive than the topological closure, and the ‘elsewhere’, or ‘difference’, operator is more expressive than the ‘somewhere’ operator. In 2014, Kudinov and Shehtman asked whether the combination of closure and elsewhere becomes strictly more expressive when adding the Cantor derivative. In this paper we give an affirmative answer: in fact, the Cantor derivative alone can define properties of topological spaces not expressible with closure and elsewhere. To prove this, we develop a novel theory of morphisms which preserve formulas with the elsewhere operator.
Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2025 Electronic address http://dx.doi.org/10.1017/S1755020322000120
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