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math.LO2026
Conceptual completeness for subgeometric logics
Ivan Di Liberti, Umberto Tarantino, Lingyuan Ye
We explore the notion of conceptual completeness for a fragment of geometric logic in the framework developed by the first and third author. Unlike its traditional interpretation a…
math.LO2026
Craig Interpolation for Subgeometric Logics
Ivan Di Liberti, Lingyuan Ye
We show that a vast class of finitary fragments of geometric logic admit a form of Craig interpolation property. In doing so, we provide a new dictionary to import technology from…
math.LO2025
Logic and Concepts in the 2-category of Topoi
Ivan Di Liberti, Lingyuan Ye
We use Kan injectivity to axiomatise concepts in the 2-category of topoi. We showcase the expressivity of this language through many examples, and we establish some aspects of the…