Craig Interpolation for Subgeometric Logics

TL;DR

This paper demonstrates that many finitary fragments of geometric logic possess a form of Craig interpolation, bridging algebraic and categorical logic techniques.

Contribution

It introduces a new approach to establish Craig interpolation in subgeometric logics by translating algebraic logic methods into categorical logic.

Findings

Many finitary geometric logic fragments admit Craig interpolation.

A new framework connects algebraic and categorical logic techniques.

The approach broadens the applicability of interpolation results.

Abstract

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 algebraic logic to categorical logic.