Interpolation in Knowledge Representation
Jean Christoph Jung, Patrick Koopmann, Matthias Knorr
TL;DR
This work surveys Craig interpolation and uniform interpolation within knowledge representation, with emphasis on description logics and logic programming. It analyzes both theoretical existence results and practical methods for computing interpolants, and discusses applications such as forgetting, modularization, explanation, abduction, and learning. The paper connects interpolation to ontology design and data reuse, highlighting when interpolants may not exist and how to proceed. It outlines a structured examination of DL foundations, uniform interpolation for ontologies, concept-level interpolation, and LP perspectives, pointing toward future directions in KR interpolation research.
Abstract
Craig interpolation and uniform interpolation have many applications in knowledge representation, including explainability, forgetting, modularization and reuse, and even learning. At the same time, many relevant knowledge representation formalisms do in general not have Craig or uniform interpolation, and computing interpolants in practice is challenging. We have a closer look at two prominent knowledge representation formalisms, description logics and logic programming, and discuss theoretical results and practical methods for computing interpolants.