知识表示中的插值方法研究 (Interpolation in Knowledge Representation)

from arxiv, The article will appear in Balder ten Cate, Jean Christoph Jung, Patrick Koopmann, Christoph Wernhard and Frank Wolter, editors. Theory and Applications of Craig Interpolation. Ubiquity Press, 2026

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.

翻译：Craig插值与一致插值在知识表示领域具有广泛的应用，包括可解释性、知识遗忘、模块化与重用，乃至学习任务。然而，许多相关的知识表示形式化方法通常并不具备Craig插值或一致插值性质，且在实际计算插值项时面临诸多挑战。本文聚焦于两种重要的知识表示形式化方法——描述逻辑与逻辑编程，系统探讨计算插值项的理论成果与实践方法。