根岑逻辑演绎思想的主要特征和哲学影响探析

An Analysis on the Characteristics and Philosophic Significances of Gentzen's Thoughts on Logical Deductions

论文在梳理根岑如何从逻辑公理化思想出发发展出自然演绎和矢列演算思想的基础上,总结出根岑逻辑演绎思想的主要特征。根岑对联接词引入和消去规则各自角色的理解及其采取的树形证明方式引导他发现并证明了切割消去定理。最后指出根岑的逻辑演绎思想对证明论语义学和意义理论有重要应用和哲学影响。

This paper shows that how Gentzen develop his own ideas on logical deductions from axiomatic system to natural deduction,and then to sequent calculus. After summarizing the main characteristics of Gentzen＇s thoughts on logical deduction,we conclude that it was his deep understanding on the functions of the introduction and elimination rule for each connectives and the tree proof style he adopted led him to discover and prove the cut- elimination theorem. Finally,we explored how Gentzen＇s ideas on logical deduction to enlighten the proof- theoretic semantics and to be applied on meaning theory.