Negation on the Australian Plan

Franz Berto; Greg Restall

doi:10.1007/s10992-019-09510-2

Negation on the Australian Plan

Franz Berto, Greg Restall

Philosophy

Research output: Contribution to journal › Article › peer-review

Abstract

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan.

Original language	English
Journal	Journal of Philosophical Logic
Volume	In press
Early online date	22 Apr 2019
DOIs	https://doi.org/10.1007/s10992-019-09510-2
Publication status	E-pub ahead of print - 22 Apr 2019

Keywords

Negation
Compatibility semantics
Kripke semantics
Non-classical logics
Many-valued logics
Modal logics

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10.1007/s10992-019-09510-2Licence: CC BY

Berto-Restall_2019_JPL_NegationAustralianPlan_CCBY-VoR
© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Final published version, 438 KBLicence: CC BY

Franz Berto
- fb96st-andrews.acuk
- Philosophy - Professor of Logic and Metaphysics
- Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology - Director
Person: Academic

Cite this

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title = "Negation on the Australian Plan",

abstract = "We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan.",

keywords = "Negation, Compatibility semantics, Kripke semantics, Non-classical logics, Many-valued logics, Modal logics",

author = "Franz Berto and Greg Restall",

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N2 - We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan.

AB - We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan.

KW - Negation

KW - Compatibility semantics

KW - Kripke semantics

KW - Non-classical logics

KW - Many-valued logics

KW - Modal logics

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M3 - Article

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VL - In press

JO - Journal of Philosophical Logic

JF - Journal of Philosophical Logic

ER -

Negation on the Australian Plan

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Franz Berto

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