Maehara Interpolation in Extensions of R-mingle

TL;DR

This paper classifies certain algebraic structures related to R-mingle logic, showing their properties and providing a decision procedure for the Maehara interpolation property in extensions.

Contribution

It provides a complete classification of quasivarieties of Sugihara algebras with specific properties and links these to logical interpolation properties.

Findings

Exactly five quasivarieties of Sugihara algebras have the amalgamation property.

All these quasivarieties have the relative congruence extension property.

Decidability of the Maehara interpolation property for finitely based extensions of R-mingle.

Abstract

We show that there are exactly five quasivarieties of Sugihara algebras with the amalgamation property, and that all of these have the relative congruence extension property. As a consequence, we obtain that the amalgamation property and transferable injections property coincide for arbitrary quasivarieties of Sugihara algebras. These results provide a complete description of arbitrary (not merely axiomatic) extensions of the logic R-mingle that have the Maehara interpolation property, and further demonstrates that the Robinson property and Maehara interpolation property coincide for arbitrary extensions of R-mingle. Further, we show that the question of whether a given finitely based extension of R-mingle has the Maehara interpolation property is decidable.