Interpolation and Amalgamation

TL;DR

This survey explores the connections between interpolation properties in various propositional logics and amalgamation properties in algebraic structures, using universal algebra to unify and illustrate these relationships across logic and algebra.

Contribution

It provides a comprehensive overview of the bridges between logical interpolation and algebraic amalgamation, demonstrating their applications in logic and algebra through numerous examples.

Findings

Identifies key relationships between interpolation and amalgamation properties.

Shows how universal algebra frameworks unify logic and algebraic structures.

Provides examples illustrating the use of these bridges in establishing properties.

Abstract

This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and amalgamation properties for corresponding classes of algebraic structures. These bridges are developed in the framework of universal algebra and illustrated with a broad range of examples from logic and algebra, demonstrating their use in establishing properties for both fields.