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.

Report

During my IVC fellowship, my main productive activity was to complete and submit two papers. The first, "Topics in Relevant Logic: A Semantic Perspective" lays the groundwork for a theory of topics inspired by the algebraic semantics for relevant logics. This paper argues for this representation of topics, and lays out the basic machinery for working with topics which I will develop in future work. The second paper, "Negated Implications in Connexive Relevant Logics'', investigates the class of relevant logics expanded by principles of connexive logics, and studies the phenomenon in such logics that they tend to prove every negated implication formula. In addition, I gave talks at the IVC Philosophy of Science Colloquium, organized by Institute Vienna Circle and Institute of Philosophy of the University of Vienna, and during a visit to the Institute of Computer Science of the Czech Academy of Sciences in Prague. Furthermore, I organised a workshop, ``Perspectives in Logic and Philosophy II'', during 08.02--09.02.2024, featuring talks from visitors from the US, UK, Italy, and the Czech Republic.