Structural completeness in propositional logics of dependence

TL;DR

This paper proves that certain propositional logics of dependence, including propositional dependence logic and inquisitive logic, are structurally complete under specific substitution classes, with related results for negative variants of intermediate logics.

Contribution

It establishes the structural completeness of key dependence logics under particular substitution classes, extending understanding of their logical properties.

Findings

Dependence logics are structurally complete under specific substitutions.

Negative variants of intermediate logics also exhibit structural completeness.

Results connect dependence logics with classical intermediate theories.

Abstract

In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a class of substitutions under which the logics are closed. We obtain an analogues result with respect to stable substitutions, for the negative variants of some well-known intermediate logics, which are intermediate theories that are closely related to inquisitive logic.