Dynamic Cantor Derivative Logic

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00557159" target="_blank" >RIV/67985807:_____/22:00557159 - isvavai.cz</a>

Result on the web

<a href="https://drops.dagstuhl.de/opus/volltexte/2022/15739/pdf/LIPIcs-CSL-2022-19.pdf" target="_blank" >https://drops.dagstuhl.de/opus/volltexte/2022/15739/pdf/LIPIcs-CSL-2022-19.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.CSL.2022.19" target="_blank" >10.4230/LIPIcs.CSL.2022.19</a>

Result language

angličtina

Original language name

Dynamic Cantor Derivative Logic

Original language description

Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as d-logics. Unlike logics based on the topological closure operator, d-logics have not previously been studied in the framework of dynamical systems, which are pairs (X, f) consisting of a topological space X equipped with a continuous function f : X → X. We introduce the logics wK4C, K4C and GLC and show that they all have the finite Kripke model property and are sound and complete with respect to the d-semantics in this dynamical setting. In particular, we prove that wK4C is the d-logic of all dynamic topological systems, K4C is the d-logic of all TD dynamic topological systems, and GLC is the d-logic of all dynamic topological systems based on a scattered space. We also prove a general result for the case where f is a homeomorphism, which in particular yields soundness and completeness for the corresponding systems wK4H, K4H and GLH. The main contribution of this work is the foundation of a general proof method for finite model property and completeness of dynamic topological d-logics. Furthermore, our result for GLC constitutes the first step towards a proof of completeness for the trimodal topo-temporal language with respect to a finite axiomatisation – something known to be impossible over the class of all spaces.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10101 - Pure mathematics

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

Article name in the collection

30th EACSL Annual Conference on Computer Science Logic

ISBN

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ISSN

1868-8969

e-ISSN

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Number of pages

17

Pages from-to

"19:1"-"19:17"

Publisher name

Schloss Dagstuhl – Leibniz-Zentrum für Informatik

Place of publication

Dagstuhl

Event location

Göttingen / Virtual

Event date

Feb 14, 2022

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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