Year: 2026
Type: article
Abstract: For a positive number a, each metric space carries the relation D a consisting of those pairs that are of distance less than a apart.A space X is said to be a-connected, if the graph (X, D a ) is connected (that is, there is a D a -path between every pair of points in X).We give a complete axiomatization of a-connected metric spaces in the language with a family of distance modalities and the universal modality.Then we give a complete axiomatization of the logic of connected (in the classical topological sense) metric spaces in the language with the topological modality, universal modality, and a single distance modality.We also show that these logics have the finite model property.
DOI: 10.4204/eptcs.447.27
Authors: John Harding, Ilya Shapirovsky
Institution: New Mexico State University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: National Science Foundation
OpenAlex ID: W7166463527
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