METRICS FOR FORMAL STRUCTURES, WITH AN APPLICATION TO KRIPKE MODELS AND THEIR DYNAMICS

Autor:	DOMINIK KLEIN, RASMUS K. RENDSVIG
Rok vydání:	2022
Předmět:	Philosophy Logic FOS: Mathematics Mathematics - Logic Logic (math.LO)
Zdroj:	The Journal of Symbolic Logic. 88:469-489
ISSN:	1943-5886 0022-4812
Popis:	The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, to formal structures serving as semantics for countable languages. The main focus is on applications to sets of pointed Kripke models, a semantics for modal logics. For the resulting metric spaces, the paper classifies topological properties including which metrics are topologically equivalent, providing sufficient conditions for compactness, characterizing clopen sets and isolated points, and characterizing the metrical topologies by a concept of logical convergence. We then apply the approach to maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing for an interpretation of the iterated updates as discrete time dynamical systems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9536ef652b38c619a120616ca5c033d8 https://doi.org/10.1017/jsl.2022.74 Zobrazit plný text záznamu