具有经典力量的非经典真理。HYPE上合成真值的证明理论分析
Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over HYPE
摘要：
关于经典与非经典真理理论的证明论强度的问题最近受到了一些关注。一个特别方便的案例研究涉及经典和非经典公理化的不动点语义。众所周知，四值或三值逻辑中的非经典公理化比经典公理化弱得多。在本文中，我们考虑增加一个合适的条件，一级蕴涵-最近研究的Hannes Leitgeb的标签下的“HYPE”的逻辑。我们特别表明，通过制定理论PKF HYPE得到一个理论，这是健全的固定点模型，而被证明理论上等同于其经典的对应KF。此外，我们还建立了它的示意性扩展-在Feferman的意义上-是强大的KF的示意性扩展，从而匹配的强度预测分析。
英文摘要：
Questions concerning the proof-theoretic strength of classical versus non-classical 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.
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