Truth values and proof theory

Greg Restall

doi:10.1007/s11225-009-9197-y

Truth values and proof theory

Greg Restall^*

^*Corresponding author for this work

Philosophy

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

28 Citations (Scopus)

Abstract

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

Original language	English
Pages (from-to)	241-264
Number of pages	24
Journal	Studia Logica
Volume	92
Issue number	2
DOIs	https://doi.org/10.1007/s11225-009-9197-y
Publication status	Published - Jul 2009

Keywords

Completeness
Intuitionistic logic
Modal logic
Proof
Sequent calculus
Truth value

Access to Document

10.1007/s11225-009-9197-y

Cite this

@article{99d57af8a556499980d036882be97085,

title = "Truth values and proof theory",

abstract = "I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.",

keywords = "Completeness, Intuitionistic logic, Modal logic, Proof, Sequent calculus, Truth value",

author = "Greg Restall",

note = "Funding Information: Acknowledgements. Thanks to the Logic Seminar at the University of Melbourne for comments on an earlier presentation of the paper, to Shawn Standefer for helpful discussions on a draft of the paper, and to two anonymous referees of the journal for many helpful questions and comments. This research is supported by the Australian Research Council, through grant DP0343388, and the Penguin Caf{\'e} Orchestra. Comments on this paper have been posted at http://consequently.org/writing/tvpt, and readers are encouraged to join the discussion.",

year = "2009",

month = jul,

doi = "10.1007/s11225-009-9197-y",

language = "English",

volume = "92",

pages = "241--264",

journal = "Studia Logica",

issn = "0039-3215",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - Truth values and proof theory

AU - Restall, Greg

N1 - Funding Information: Acknowledgements. Thanks to the Logic Seminar at the University of Melbourne for comments on an earlier presentation of the paper, to Shawn Standefer for helpful discussions on a draft of the paper, and to two anonymous referees of the journal for many helpful questions and comments. This research is supported by the Australian Research Council, through grant DP0343388, and the Penguin Café Orchestra. Comments on this paper have been posted at http://consequently.org/writing/tvpt, and readers are encouraged to join the discussion.

PY - 2009/7

Y1 - 2009/7

N2 - I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

AB - I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

KW - Completeness

KW - Intuitionistic logic

KW - Modal logic

KW - Proof

KW - Sequent calculus

KW - Truth value

UR - http://www.scopus.com/inward/record.url?scp=70349562493&partnerID=8YFLogxK

U2 - 10.1007/s11225-009-9197-y

DO - 10.1007/s11225-009-9197-y

M3 - Article

AN - SCOPUS:70349562493

SN - 0039-3215

VL - 92

SP - 241

EP - 264

JO - Studia Logica

JF - Studia Logica

IS - 2

ER -

Truth values and proof theory

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this