2026-07-23T04:09:10Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15739 2024-03-06T10:56:05Z ddc:004 open_access

Dynamic Cantor Derivative Logic Fernández-Duque, David Montacute, Yoàv dynamic topological logic Cantor derivative temporal logic modal logic 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 T_D 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik David Fernández-Duque and Yoàv Montacute 2022 Is Part Of LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2022.19 urn:nbn:de:0030-drops-157397 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.19 eng https://creativecommons.org/licenses/by/4.0/legalcode