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Interpolation in Knowledge Representation

arXiv 2512.08833 ↗First posted 9 Dec 2025cs.AI cs.LOcited by 0

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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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 25 of its 139 references that are in the map. First posted on arXiv 9 Dec 2025.

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References · 25

  1. 2017Multi-shot ASP solving with clingocited by 115
  2. 2021Learning Description Logic Ontologies. Five Approaches. Where Do They Stand?cited by 12
  3. 2018Answering the "why" in Answer Set Programming - A Survey of Explanation Approachescited by 11
  4. 2020Logical Separability of Labeled Data Examples under Ontologiescited by 10
  5. 2020Signature-Based Abduction for Expressive Description Logics -- Technical Reportcited by 9
  6. 2020Omission-based Abstraction for Answer Set Programscited by 7
  7. 2018The Data Complexity of Ontology-Mediated Queries with Closed Predicatescited by 5
  8. 2021Separating Data Examples by Description Logic Concepts with Restricted Signaturescited by 5
  9. 2021Forgetting in Answer Set Programming -- A Surveycited by 5
  10. 2018Inseparability and Conservative Extensions of Description Logic Ontologies: A Surveycited by 4
  11. 2019A Syntactic Operator for Forgetting that Satisfies Strong Persistencecited by 4
  12. 2023Efficient Computation of General Modules for ALC Ontologies (Extended Version)cited by 4
13 more
  1. 2014Interpolable Formulas in Equilibrium Logic and Answer Set Programmingcited by 2
  2. 2020Living Without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusionscited by 2
  3. 2020Conservative Extensions in Horn Description Logics with Inverse Rolescited by 2
  4. 2021On Free Description Logics with Definite Descriptionscited by 2
  5. 2022Interpolants and Explicit Definitions in Extensions of the Description Logic ELcited by 1
  6. 2024Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logiccited by 1
  7. 2024The interpolant existence problem for weak K4 and difference logiccited by 1
  8. 2024Constructive Interpolation and Concept-Based Beth Definability for Description Logics via Sequentscited by 1
  9. 2025Interpolation with Automated First-Order Reasoningcited by 1
  10. 2025Computation of Interpolants for Description Logic Concepts in Hard Casescited by 1
  11. 2025Interpolation in Classical Propositional Logiccited by 1
  12. 2025Interpolation in First-Order Logiccited by 1
  13. 2025Six Proofs of Interpolation for the Modal Logic Kcited by 1

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