Interpolation in Knowledge Representation

TL;DR

This paper explores the role of Craig and uniform interpolation in knowledge representation, focusing on description logics and logic programming, highlighting theoretical insights and practical methods for computing interpolants.

Contribution

It provides a comparative analysis of interpolation concepts in description logics and logic programming, addressing theoretical challenges and practical computation methods.

Findings

Interpolation facilitates explainability, forgetting, modularization, and reuse in knowledge representation.

Many formalisms lack interpolation, and computing it is often difficult.

The paper discusses theoretical results and practical algorithms for interpolant computation.

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.