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

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...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of symbolic logic 2023-06, Vol.88 (2), p.469-489
Main Authors: KLEIN, DOMINIK, RENDSVIG, RASMUS K.
Format: Article
Language:English
Subjects:
Codes
Dynamical systems
Epistemology
Kripke, Saul
Language
Logic
Semantics
System theory
Valuation
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-4812
1943-5886
DOI:10.1017/jsl.2022.74