King's College London

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 -