“Geometric Models for Relevant Logics”, article in progress.
You are welcome to download and read this document. I especially welcome feedback on it. As it is not yet published in final form, if you want to cite the paper, please check with me first. Thanks.
Alasdair Urquhart’s work on models for relevant logics is distinctive in a number of different ways. One key theme, present in both his undecidability proof for the relevant logic R, and his proof of the failure of interpolation in R, is the use of techniques from geometry. In this paper, inspired by Urquhart’s work, I explore ways to generate natural models of R from geometries, and different constraints that an accessibility relation in such a model might satisfy. I end by showing that a set of natural conditions on an accessibility relation, motivated by geometric considerations, is jointly unsatisfiable.
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.