# Interpolation in Knowledge Representation

arXiv: https://arxiv.org/abs/2512.08833 · HTML: https://mlsanity.com/paper/2512.08833/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 139 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 25 of 25)

- [Multi-shot ASP solving with clingo](https://mlsanity.com/paper/1705.09811/) (2017)
- [Learning Description Logic Ontologies. Five Approaches. Where Do They Stand?](https://mlsanity.com/paper/2104.01193/) (2021)
- [Answering the "why" in Answer Set Programming - A Survey of Explanation Approaches](https://mlsanity.com/paper/1809.08034/) (2018)
- [Logical Separability of Labeled Data Examples under Ontologies](https://mlsanity.com/paper/2007.01610/) (2020)
- [Signature-Based Abduction for Expressive Description Logics -- Technical Report](https://mlsanity.com/paper/2007.00757/) (2020)
- [Omission-based Abstraction for Answer Set Programs](https://mlsanity.com/paper/2004.01410/) (2020)
- [The Data Complexity of Ontology-Mediated Queries with Closed Predicates](https://mlsanity.com/paper/1809.00134/) (2018)
- [Separating Data Examples by Description Logic Concepts with Restricted Signatures](https://mlsanity.com/paper/2107.05285/) (2021)
- [Forgetting in Answer Set Programming -- A Survey](https://mlsanity.com/paper/2107.07016/) (2021)
- [Inseparability and Conservative Extensions of Description Logic Ontologies: A Survey](https://mlsanity.com/paper/1804.07805/) (2018)
- [A Syntactic Operator for Forgetting that Satisfies Strong Persistence](https://mlsanity.com/paper/1907.12501/) (2019)
- [Efficient Computation of General Modules for ALC Ontologies (Extended Version)](https://mlsanity.com/paper/2305.09503/) (2023)
- [Interpolable Formulas in Equilibrium Logic and Answer Set Programming](https://mlsanity.com/paper/1401.3897/) (2014)
- [Living Without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusions](https://mlsanity.com/paper/2007.02736/) (2020)
- [Conservative Extensions in Horn Description Logics with Inverse Roles](https://mlsanity.com/paper/2011.09858/) (2020)
- [On Free Description Logics with Definite Descriptions](https://mlsanity.com/paper/2106.15513/) (2021)
- [Interpolants and Explicit Definitions in Extensions of the Description Logic EL](https://mlsanity.com/paper/2202.07186/) (2022)
- [Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logic](https://mlsanity.com/paper/2402.07696/) (2024)
- [The interpolant existence problem for weak K4 and difference logic](https://mlsanity.com/paper/2403.11255/) (2024)
- [Constructive Interpolation and Concept-Based Beth Definability for Description Logics via Sequents](https://mlsanity.com/paper/2404.15840/) (2024)
- [Interpolation with Automated First-Order Reasoning](https://mlsanity.com/paper/2507.01577/) (2025)
- [Computation of Interpolants for Description Logic Concepts in Hard Cases](https://mlsanity.com/paper/2507.15689/) (2025)
- [Interpolation in Classical Propositional Logic](https://mlsanity.com/paper/2508.11449/) (2025)
- [Interpolation in First-Order Logic](https://mlsanity.com/paper/2510.03822/) (2025)
- [Six Proofs of Interpolation for the Modal Logic K](https://mlsanity.com/paper/2510.16398/) (2025)

## Abstract (arXiv)

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.