Abductive Spaces: Modeling Concept Framework Revision with Category Theory

Abstract

A formal model of abductive inference is provided in which abduction is conceived as expansive and contractive movements through a topological space of theoretical and practical commitments. A pair of presheaves over the (Heyting algebra) space of commitments corresponds to communities sharing commitments on the one hand and possible obstructions to commitments on the other. In this framework, abductive inference is modeled by the dynamics of redistributed communities of commitment made in response to obstructive encounters. This semantic-pragmatic model shows how elementary category theory tools can be used to formalize abductive inference while hewing close to ordinary intuitions about collective agency and reasoning.