直觉主义逻辑上的公理化真理论  

Axiomatic Theories of Truth on Intuitionistic Logic

作　　者：李娜[1] 李晟[1] 

机构地区：[1]南开大学哲学院

出　　处：《逻辑学研究》2015年第3期48-63,共16页Studies in Logic

基　　金：国家社会科学基金项目"公理化真理论研究"(12BZX059)

摘　　要：本文在直觉主义逻辑和海廷算术HA的基础上,重新考察了去引号模式和组合真公理,得到了三种直觉主义的类型真理论:IDT、ICT和SICT,并探讨了它们的一些基本性质。本文证明了三者都满足对算术的标准解释,并且IDT和SICT是实质上充分的真理论,而ICT不是。在保守性方面,本文证明了IDT是HA的算术保守扩充理论,而SICT是非保守扩充。In this paper, we investigate the disquotation scheme and the compositional axioms of truth based on the intuitionistic logic and Heyting arithmetic HA. Three intuitionistic typed theories of truth, that is, IDT, ICT and SICT, will be obtained and their basic properties will be discussed. The main results of this paper are the standard interpretation of arithmetic is suitable for all of them, IDT and SICT are both theories of truth meet adequacy conditions, and IDT is conservative over HA, but SICT not.

关 键 词：直觉主义逻辑 公理化真理论 类型 去引号 组合 

分 类 号：B023.3[哲学宗教—哲学理论]