5月26日小野寛晰教授讲座：Proof-theoretic approach to logic ― an introduction
来源：会议讲座
作者：
时间：2015-05-24
主讲人：Hiroakira Ono （小野寛晰 教授）
题目： Emeritus professor of Japan Advanced Institute of Science and Technology
报告时间地点： 5月26日(周二）下午15:10-18:00，北京大学二教525室
摘要：
This is an introductory talk on proof theory, which is one of most important branches of mathematical logic. Proof-theoretic approach is complementary to semantical one, and its subject is to study structures of proofs, or formal derivations, in formal systems, like Hilbert systems, natural deductions and sequent calculi.
To begin with, I will give a brief sketch of the history of proof theory in its early stage, dated back to the attempt by D. Hilbert to show the consistency of mathematics. Then, I will explain significant contributions to proof theory by G. Gentzen in the 1930s, who introduced both natural deductions and sequent systems, and showed fundamental results on “normal proofs”. In the last part of my talk, I will touch on topics of the study in recent years, which includes developments of “substructural logics”, in which Gentzen’s sequent formulation plays an essential role.
In my talk, I will focus my attention more on its background ideas and motivations, and not going into technical details so much.
主讲人简介：
小野寛晰教授是国际著名数理逻辑学家，研究兴趣包括证明论，逻辑的代数方法等，在子结构逻辑领域中做出了杰出的贡献。小野教授是多家顶级逻辑学国际期刊的编委，曾任北陆先端科学技术大学院大学（JAIST）副校长。
个人主页：http://www.jaist.ac.jp/is/labs/ono-ishihara-lab/ono-lab/
题目： Emeritus professor of Japan Advanced Institute of Science and Technology
报告时间地点： 5月26日(周二）下午15:10-18:00，北京大学二教525室
摘要：
This is an introductory talk on proof theory, which is one of most important branches of mathematical logic. Proof-theoretic approach is complementary to semantical one, and its subject is to study structures of proofs, or formal derivations, in formal systems, like Hilbert systems, natural deductions and sequent calculi.
To begin with, I will give a brief sketch of the history of proof theory in its early stage, dated back to the attempt by D. Hilbert to show the consistency of mathematics. Then, I will explain significant contributions to proof theory by G. Gentzen in the 1930s, who introduced both natural deductions and sequent systems, and showed fundamental results on “normal proofs”. In the last part of my talk, I will touch on topics of the study in recent years, which includes developments of “substructural logics”, in which Gentzen’s sequent formulation plays an essential role.
In my talk, I will focus my attention more on its background ideas and motivations, and not going into technical details so much.
主讲人简介：
小野寛晰教授是国际著名数理逻辑学家，研究兴趣包括证明论，逻辑的代数方法等，在子结构逻辑领域中做出了杰出的贡献。小野教授是多家顶级逻辑学国际期刊的编委，曾任北陆先端科学技术大学院大学（JAIST）副校长。
个人主页：http://www.jaist.ac.jp/is/labs/ono-ishihara-lab/ono-lab/