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Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over hype.

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Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over hype. / Nicolai, Carlo; Fischer, Martin; Dopico Fernandez, Pablo.

In: Review Of Symbolic Logic, 25.03.2021, p. 1-26.

Research output: Contribution to journalArticlepeer-review

Harvard

Nicolai, C, Fischer, M & Dopico Fernandez, P 2021, 'Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over hype.', Review Of Symbolic Logic, pp. 1-26. https://doi.org/10.1017/S1755020321000137

APA

Nicolai, C., Fischer, M., & Dopico Fernandez, P. (2021). Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over hype. Review Of Symbolic Logic, 1-26. https://doi.org/10.1017/S1755020321000137

Vancouver

Nicolai C, Fischer M, Dopico Fernandez P. Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over hype. Review Of Symbolic Logic. 2021 Mar 25;1-26. https://doi.org/10.1017/S1755020321000137

Author

Nicolai, Carlo ; Fischer, Martin ; Dopico Fernandez, Pablo. / Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over hype. In: Review Of Symbolic Logic. 2021 ; pp. 1-26.

Bibtex Download

@article{ca193240a5714331a1e8567dc672a740,
title = "Nonclassical truth with classical strength.: A proof-theoretic analysis of compositional truth over hype.",
abstract = "Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First- Degree Entailment – a logic recently studied by Hannes Leitgeb under the label HYPE. We show in particular that, by formulating the theory PKF over HYPE, one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF. Moreover, we establish that also its schematic extension – in the sense of Feferman – is as strong as the schematic extension of KF, thus matching the strength of predicative analysis.",
author = "Carlo Nicolai and Martin Fischer and {Dopico Fernandez}, Pablo",
year = "2021",
month = mar,
day = "25",
doi = "10.1017/S1755020321000137",
language = "English",
pages = "1--26",
journal = "Review Of Symbolic Logic",
issn = "1755-0203",
publisher = "Cambridge University Press",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - Nonclassical truth with classical strength.

T2 - A proof-theoretic analysis of compositional truth over hype.

AU - Nicolai, Carlo

AU - Fischer, Martin

AU - Dopico Fernandez, Pablo

PY - 2021/3/25

Y1 - 2021/3/25

N2 - Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First- Degree Entailment – a logic recently studied by Hannes Leitgeb under the label HYPE. We show in particular that, by formulating the theory PKF over HYPE, one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF. Moreover, we establish that also its schematic extension – in the sense of Feferman – is as strong as the schematic extension of KF, thus matching the strength of predicative analysis.

AB - Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First- Degree Entailment – a logic recently studied by Hannes Leitgeb under the label HYPE. We show in particular that, by formulating the theory PKF over HYPE, one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF. Moreover, we establish that also its schematic extension – in the sense of Feferman – is as strong as the schematic extension of KF, thus matching the strength of predicative analysis.

UR - http://www.scopus.com/inward/record.url?scp=85103265501&partnerID=8YFLogxK

U2 - 10.1017/S1755020321000137

DO - 10.1017/S1755020321000137

M3 - Article

SP - 1

EP - 26

JO - Review Of Symbolic Logic

JF - Review Of Symbolic Logic

SN - 1755-0203

ER -

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