Logic and Computation II
Based on the subjects we learned in the previous semester (1. computable functions; 2. complexity theory; 3. first-order logic), we will move on to more advanced topics on modal logic, infinite automata, desciriptive set theory, etc.
讲师
日期
2025年03月04日 至 05月29日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 15:20 - 16:55 | A3-2-301 | ZOOM 09 | 230 432 7880 | BIMSA |
修课要求
"Logic and Computation I" or equivalent knowledge of mathematical logic and theory of computation.
课程大纲
4. Modal logic
Kripke models, Kripke-complete and canonical logics, standard translation, bisimulation, decidability results, and epistemic logic.
5. Mu-calculus
Second-order logic, inductive operators, Modal mu-calculus and game semantics, alternation hierarcy, applications to temporal logics.
6. Automata on infite objects
Buechi automata and S1S, tree automata and S2S, finite model theory and parity games.
7. Recursion-theoretic hierarchies
Oracle computation, m-degrees and T-degrees, arithmetical and analytical hierarchies,
descriptive set theory.
"Logic and Computation III" will cover further advanced topics related to second-order arithmetic and admissible set theory.
Kripke models, Kripke-complete and canonical logics, standard translation, bisimulation, decidability results, and epistemic logic.
5. Mu-calculus
Second-order logic, inductive operators, Modal mu-calculus and game semantics, alternation hierarcy, applications to temporal logics.
6. Automata on infite objects
Buechi automata and S1S, tree automata and S2S, finite model theory and parity games.
7. Recursion-theoretic hierarchies
Oracle computation, m-degrees and T-degrees, arithmetical and analytical hierarchies,
descriptive set theory.
"Logic and Computation III" will cover further advanced topics related to second-order arithmetic and admissible set theory.
参考资料
[1] H.D. Ebbinghaus, H. Flum and W. Thomas, Mathematical Logic, 3rd ed., Springer 2021.
[2] D.C. Kozen, Theory of Computation, Springer 2006.
[3] P. Blackburn, M. de Rijke and Y. Venema, Modal Logic, Cambridge UP, 2002.
[4] K. Tanaka, 計算理論と数理論理学 (Mathematics of Logic and Computation, in Japanese), Kyoritsu 2022.
[2] D.C. Kozen, Theory of Computation, Springer 2006.
[3] P. Blackburn, M. de Rijke and Y. Venema, Modal Logic, Cambridge UP, 2002.
[4] K. Tanaka, 計算理論と数理論理学 (Mathematics of Logic and Computation, in Japanese), Kyoritsu 2022.
听众
Advanced Undergraduate
, Graduate
视频公开
不公开
笔记公开
公开
语言
英文
讲师介绍
田中一之教授博士毕业于美国加州大学伯克利分校，曾就职于东京工业大学和东北大学，并指导15位博士生和50名硕士生，2022年正式入职BIMSA。他是数理逻辑和计算理论领域的国际知名学者，在反推数学和二阶算术领域开创了新的研究方法，如WKLo的田中嵌入定理和守恒结果的田中公式，取得了一系列奠基性的成果，并将这一研究方向引入日本，将日本的数理逻辑研究推向了世界水平。田中一之教授还致力于模态mu演算，认知逻辑，随机博弈树等交叉领域的研究。