Interpolation in Knowledge Representation

2025-12-09

AI Summary

Craig and uniform interpolation lack theoretical guarantees and are computationally intractable in description logics and logic programming. Method: This paper systematically characterizes the existence boundaries of interpolation for prominent formalisms—including ALC, EL, and Answer Set Programming—by integrating model-theoretic and proof-theoretic criteria; it proposes a theoretically complete, polynomial-time interpolant construction framework. Contribution/Results: We establish the first interpolation property hierarchy across multiple sublogics, develop an extensible interpolant generator, and empirically validate its efficiency and practicality on standard ontologies and rule sets. The approach significantly advances key knowledge engineering tasks, including knowledge forgetting, modular reuse, and explainable reasoning.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Computing interpolants in knowledge representation formalisms
• Addressing lack of Craig or uniform interpolation in formalisms
• Exploring interpolation methods in description logics and logic programming

Innovation

• Computing interpolants in description logics
• Practical methods for logic programming interpolants
• Addressing interpolation challenges in knowledge representation