Six Proofs of Interpolation for the Modal Logic K

2025/10/18 by Nick Bezhanishvili, Balder ten Cate, Bezhanishvili, Nick +3 · 2 citations
Computer Science · #Advanced Algebra and Logic #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.2510.16398

openalex publication_date 2025/10/18 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28

Abstract

In this chapter, we present six different proofs of Craig interpolation for the modal logic K, each using a different set of techniques (model-theoretic, proof-theoretic, syntactic, automata-theoretic, using quasi-models, and algebraic). We compare the pros and cons of each proof technique.

Citations

• Separation and Definability in Fragments of Two-Variable First-Order Logic with Counting
• Interpolation in extensions of first-order logic

Cited by

• Interpolation via Generalized Splitting
• Interpolation in Knowledge Representation

Related

• A non-uniform view of Craig interpolation in modal logics with linear frames
• Interpolation in Non-Classical Logics
• Interpolation in First-Order Logic
• Deciding the Existence of Interpolants and Definitions in First-Order Modal Logic
• A proof-theoretic approach to uniform interpolation property of multi-agent modal logic