Unary interpretability logics for sublogics of the interpretability logic $\mathbf{IL}$

TL;DR

This paper explores unary interpretability logics, identifying unary counterparts for sublogics of the binary interpretability logic IL, thereby advancing the understanding of interpretability logic structures.

Contribution

It introduces the unary counterparts of the sublogics of IL, expanding the framework of unary interpretability logics.

Findings

Identified unary counterparts for all sublogics of IL

Extended the framework of unary interpretability logics

Provided new insights into the structure of interpretability logics

Abstract

De Rijke introduced a unary interpretability logic $\mathbf{il}$, and proved that $\mathbf{il}$ is the unary counterpart of the binary interpretability logic $\mathbf{IL}$. In this paper, we find the unary counterparts of the sublogics of $\mathbf{IL}$.