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报告内容简介：
Computability is one of the most interesting and fundamental concepts in mathematics, philosophy and computer science, and it would be more than natural to ask what logic it induces. This is where computability logic comes in. It is a semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which logic has more traditionally been. It was introduced by the speaker very recently and, at present, still remains in its infancy stage, with open problems prevailing over answered questions. The area is largely a virgin soil providing plenty of research opportunities, with good chances of interesting findings, for those with interests in logic and its applications in computer science.
On the philosophical side, computability logic offers a new view of what logical operators mean, and how the abstract speculations of constructivism can find a materialization in the form of an intuitively convincing and mathematically strict logical semantics. It also offers a way to reconcile and unify various competing or antagonistic traditions of logical thought such as classical, intuitionistic and linear logics.
The goal of this presentation is to introduce the basic concepts, motivations and philosophy of computability logic, to overview the current situation in the area and discuss some possible future developments.
可计算性在数学、哲学和计算机科学领域是最有趣和最基础的概念之一，人们很自然地会问，从可计算性得出的是什么逻辑，这就是报告人新近提出的可计算性逻辑。可计算性逻辑是一种语义研究的平台，同时也是一项宏伟计划，试图将逻辑发展为一种可计算性的形式理论，反对传统的逻辑是真之形式理论的观念。可计算性逻辑目前是一个崭新的研究领域，由于在逻辑学和计算机科学上的广泛应用，将为研究者提供广阔的研究空间。
在哲学方面，可计算性逻辑提出了对逻辑算子涵义的新观点；并且说明如何以一种直觉上可信、数学上严格的逻辑语义学的形式为构造主义抽象的理论推测提供可实现的途径；同时对各种逻辑传统（如经典逻辑、直觉主义逻辑和线性逻辑等），给出一种统一和融和的方法。报告主要介绍可计算性逻辑的基本概念、理论动因以及相关的哲学问题，概述其研究现状，讨论其未来可能的发展。
报告人简介：
Giorgi Japaridze, 美国维拉诺瓦大学计算机系终身教授, 莫斯科大学逻辑学博士，宾夕法尼亚大学计算机科学博士，阿姆斯特丹大学数学与计算机科学系博士后。曾担任格鲁吉亚科学院哲学研究所资深研究员，美国圣母大学访问教授。他的工作集中在可证明逻辑领域，曾解决了一些大的难题，提出了tolerance, cotolerance和 cointerpretability等新概念。最近在美国国家科学基金的资助下又提出了三个新的研究方向：computability logic, cirquent calculus, 和 abstract resource semantics，受到逻辑学界和计算理论学界的高度关注。Japaridze教授在“Annals of Pure and Applied Logic”,“Journal of Symbolic Logic”,“Theoretical Computer Science”,“Transactions on Computational Logic”以及“Journal of Logic and Computation”等世界权威期刊发表了大量论文。他的论文在 APAL 和 JLC上被广泛引用。 |
