Revisiting Interpolation in Relevant Logics

TL;DR

This paper investigates the interpolation property in relevant logics, identifying two maximal extensions of R and demonstrating that one possesses a strong form of interpolation, thus providing a notable example in the field.

Contribution

The paper establishes the existence of two maximal extensions of relevant logic R and proves that one has a strong interpolation property, a novel result in relevant logic research.

Findings

Identified exactly two maximal schematic extensions of relevant logic R.

Proved that one extension has a strong form of interpolation for deducibility.

Provided the first known example of a relevant logic with interpolation.

Abstract

There are exactly two maximal schematic extensions of the relevant logic R with the variable sharing property. We establish that one of them has a strong form of interpolation for deducibility, thereby giving an example of a well-known relevant logic with interpolation.