Uniform Interpolation

2025/12/17 by van Gool, Sam
#03-02 (Primary) 03B20 03B45 03C10 03G27 03G30 06D20 (Secondary) #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #I.2.4 #Logic (math.LO) #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2512.15391

Abstract

Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic propositional logic. We outline how this theorem may be proved semantically via the definability of bisimulation quantifiers, and how it generalizes to an open mapping theorem between Esakia spaces. We also discuss connections between uniform interpolation and research in categorical logic, algebra, and model theory.

Citations

• Interpolation in Knowledge Representation
• Interpolation and Amalgamation
• Interpolation in First-Order Logic
• Interpolation in Classical Propositional Logic
• A new calculus for intuitionistic Strong Löb logic: strong termination and cut-elimination, formalised
• Uniform Lyndon interpolation for intuitionistic monotone modal logic
• Hennessy-Milner Properties via Topological Compactness
• Model completions for universal classes of algebras: necessary and sufficient conditions
• Coherence in Modal Logic
• Uniform interpolation and coherence
• Uniform interpolation and compact congruences
• Uniform interpolation and the existence of sequent calculi
• Monadic second order logic as the model companion of temporal logic
• Model-completion of varieties of co-Heyting algebras

Cited by

• Interpolation in Knowledge Representation

Related

• Uniform Interpolation in Coalgebraic Modal Logic
• Interpolation in Classical Propositional Logic
• Uniform Lyndon interpolation property in propositional modal logics
• Uniform Interpolation for Propositional and Modal Team Logics
• Interpolation in model theory