论文标题
具有古典力量的非古典真理。对炒作的组成真理的证明理论分析
Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over HYPE
论文作者
论文摘要
最近，有关古典和非古典理论的证明理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定点语义的经典和非经典公理。众所周知，四或三值逻辑中的非经典公理构成比其经典对应物弱得多。在本文中，我们考虑增加适合一级有条件的一级成果 - 汉尼斯·莱特吉布（Hannes Leitgeb）在标签“炒作”下最近研究的逻辑。我们特别表明，通过对hype的理论提出理论，可以获得相对于固定点模型的理论，而理论上证明了其经典的对应物KF。此外，我们确定其示意图扩展（从Feferman的意义上）与KF的示意图扩展一样强，因此与谓语分析的强度相匹配。
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.
