Abstract

In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the properties are satisfied by the weak relevant logics $${\textbf{B}}$$ and $${{\textbf{B}}}{{\textbf{M}}}$$, respectively. We argue that such properties address a sort of semantic lossiness of strong depth relevance.