Geometric models for relevant logics

Greg Restall

doi:10.1007/978-3-030-71430-7_6

Geometric models for relevant logics

Greg Restall^*

^*Corresponding author for this work

Philosophy

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

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 language	English
Title of host publication	Alasdair Urquhart on nonclassical and algebraic logic and complexity of proofs
Editors	Ivo Düntsch, Edwin Mares
Place of Publication	Cham
Publisher	Springer
Chapter	6
Pages	225-242
Number of pages	18
ISBN (Electronic)	9783030714307
ISBN (Print)	9783030714291, 9783030714321
DOIs	https://doi.org/10.1007/978-3-030-71430-7_6
Publication status	Published - 25 Sept 2021

Publication series

Name	Outstanding contributions to logic
Volume	22
ISSN (Print)	2211-2758
ISSN (Electronic)	2211-2766

Keywords

Frame
Geometry
Model
Relevant logic
Semantics
Substructural

Access to Document

10.1007/978-3-030-71430-7_6

Cite this

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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.",

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doi = "10.1007/978-3-030-71430-7\_6",

language = "English",

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KW - Frame

KW - Geometry

KW - Model

KW - Relevant logic

KW - Semantics

KW - Substructural

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SN - 9783030714321

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BT - Alasdair Urquhart on nonclassical and algebraic logic and complexity of proofs

A2 - Düntsch, Ivo

A2 - Mares, Edwin

PB - Springer

CY - Cham

ER -

Geometric models for relevant logics

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