Topics in Relevant Logics: A Semantic Perspective

Philosophy of Science Colloquium
The Institute Vienna Circle holds a Philosophy of Science Colloquium with talks by our present fellows.

Date: 12/10/2023

Time: 15h00

Venue: New Institute Building (NIG), Universitätsstraße 7, 1010 Wien, SR 2H

Abstract:

A recent hot topic in hyperintensional logics has been semantics which explicitly represent, and employ, topics. In such a framework, formulas are interpreted in terms not just of truth-conditions, but also in terms of their topics. This machinery allows one to define various topic-sensitive modal operators (such as Berto's Topic Sensitive Intentional Modals) which have been subject to recent investigation. Relevant logics are hyperintensional logics which have often been interpreted in a topical guise -- demanding that for a premise to entail a conclusion, the former must be relevant to the latter in the sense that the two share a common topic. This understanding of relevance is usually pinned down to Belnap's Variable Sharing Property, which is a syntactic criterion on validity usually taken as definitive of relevance. Using a semantic characterisation of Variable Sharing due to Robles and Mendez, I'll show how to understand the semantics for the relevant logic R as topical, so that R can be seen as a topic-sensitive logic in the sort of topical semantic tradition more recently developed. I'll discuss further how this semantic toolkit can be extended to apply to a range of other logics, and to define new topic-sensitive logics.