@inbook{d9007bcfe7b941cfa5209dd50adbc2fb,
title = "Geometric models for relevant logics",
abstract = "Alasdair Urquhart{\textquoteright}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{\textquoteright}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.",
keywords = "Frame, Geometry, Model, Relevant logic, Semantics, Substructural",
author = "Greg Restall",
note = "Funding: This research was supported by the Australian Research Council, Discovery Grant DP150103801.",
year = "2021",
month = sep,
day = "25",
doi = "10.1007/978-3-030-71430-7_6",
language = "English",
isbn = "9783030714291",
series = "Outstanding contributions to logic",
publisher = "Springer",
pages = "225--242",
editor = "Ivo D{\"u}ntsch and Edwin Mares",
booktitle = "Alasdair Urquhart on nonclassical and algebraic logic and complexity of proofs",
address = "Netherlands",
}