Andrew Tedder Ph.D.

2023 September 1st until 2024 February 28th

Affiliation: 

Homepage: https://sites.google.com/view/andrewjtedder/home

Research for a study about:

Topics in Relevant Logic: A Semantic Perspective

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. In the course of my research stay at the IVC, I intend to write a paper sketching an idea for how to treat of relevant logics in a topic-theoretic manner which provides a straightforward connection to recent work in the area. The target paper is intended to be the first of a sequence of papers on the area, hopefully forming the basis of a broader research project in the upcoming years. The basic idea for this `proof of concept' work is to use a semantic characterisation of Variable Sharing due to Robles and Mendez, and 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 being investigated by Berto and others.

Lecture

Topics in Relevant Logics: A Semantic Perspective

Date: 2023 October 12,

Time: 3-4.30 pm CET

Venue: 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.