Geometric Models for Relevant Logics

Greg Restall*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter


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 (Urquhart 1984) and his proof of the failure of interpolation in R (Urquhart 1993), is the use of techniques from geometry (Urquhart 2019). 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.

Original languageEnglish
Title of host publicationOutstanding Contributions to Logic
PublisherSpringer Science and Business Media B.V.
Number of pages18
Publication statusPublished - 2022

Publication series

NameOutstanding Contributions to Logic
ISSN (Print)2211-2758
ISSN (Electronic)2211-2766


  • Frame
  • Geometry
  • Model
  • Relevant logic
  • Semantics
  • Substructural


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