论文标题
希尔伯特系统的语义不完整，结合了古典和直觉的命题逻辑
Semantic Incompleteness of Hilbert System for a Combination of Classical and Intuitionistic Propositional Logic
论文作者
论文摘要
本文的更新版本已经发表在《澳大利亚逻辑杂志》上。您可以从以下链接中访问论文：https：//ojs.victoria.ac.nz/ajl/ajl/article/view/7696。 本文显示，Hilbert System $（\ Mathbf {C+J}）^{ - } $，由Del Cerro和Herzig（1996）给出，在语义上是不完整的。该系统是作为Kripke语义学的证明理论，用于直觉和经典命题逻辑的结合，这是通过将经典含义的自然语义语句添加到直觉的Kripke语义中来获得的。尽管Hilbert System $（\ Mathbf {C+J}）^{ - } $通常包含直觉的Modus Ponens，但它不包含经典的Modus Ponens。本文提出了一个论点，以确保系统$（\ Mathbf {C+J}）^{ - } $在语义上是不完整的，因为没有经典的Modus Ponens。我们的方法基于悖论的逻辑，悖论是Priest（1979）提出的一种矛盾的逻辑。
The updated version of this paper has already been published in The Australasian Journal of Logic. You can access to the paper from the following link: https://ojs.victoria.ac.nz/ajl/article/view/7696. This paper shows Hilbert system $(\mathbf{C+J})^{-}$, given by del Cerro and Herzig (1996) is semantically incomplete. This system is proposed as a proof theory for Kripke semantics for a combination of intuitionistic and classical propositional logic, which is obtained by adding the natural semantic clause of classical implication into intuitionistic Kripke semantics. Although Hilbert system $(\mathbf{C+J})^{-}$ contains intuitionistic modus ponens as a rule, it does not contain classical modus ponens. This paper gives an argument ensuring that the system $(\mathbf{C+J})^{-}$ is semantically incomplete because of the absence of classical modus ponens. Our method is based on the logic of paradox, which is a paraconsistent logic proposed by Priest (1979).
