下学期（2013年春季）我们很荣幸请到了印度数学科学研究所的Ramanujam教授在北大哲学系开设两门逻辑课程：
1 一阶逻辑的可判定片段及扩张 （2学分）周三周五的3－4节 四教403
2 博弈与逻辑选讲 （2学分）周四10－12节 四教304
课程简介及主讲人简介附后。
机会非常难得，欢迎大家选修或转发信息，注意两门课均从2013年四月第二周开始，为英文授课。
课程内容较深，需要较好的数理逻辑及模态逻辑基础，具体课程时间安排请以教务部系统为准。
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主讲人简介：
Ramaswamy Ramanujam 在印度孟买大学获得博士学位，目前是印度数理科学研究所（IMSc）的逻辑及分布式系统教授。他与Rohit Parikh教授合作的文章Distributed Processes and the Logic of Knowledge 是时态认知逻辑领域里最重要的奠基性工作之一。Ramanujam教授在各类国际顶级期刊及会议论文集上发表了数十篇高质量的学术文章，他的研究方向包括时态逻辑，认知逻辑，博弈论基础以及安全协议验证。同时，Ramanujam教授还是国际符号逻辑学会（ASL）的理事，曾任印度逻辑学会会长，是ACM计算逻辑通讯等顶级国际期刊的编辑。
个人主页：http://www.imsc.res.in/~jam/
部分文章：http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/r/Ramanujam:Ramaswamy.html
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Prof. Ramanujam's courses at PKU (2013 Spring April-June)
Course 1:
Decidable fragments and extensions of first-order logic
一阶逻辑的可判定片段及扩张
Credits: 2 points
4 hours/week, 9 weeks (April 8th - June 9th)
Classroom requirements: Blackboard+Beamer, 15 students
Assessment: course notes writing
Synopsis:
Ever since the undecidability of first order logic was established by Goedel
and Turing, the search for decidable fragments has proceeded in many
interesting directions. They are obtained by syntactic restrictions (on the
vocabulary or use of quantifiers or how they occur in the scope of
connectives) or restrictions on model classes (restricted arithmetics,
linear orders, trees etc). These have led to logics that are interesting
from many viewpoints: philosophical and computational. Their relationship
to modal logics is especially intriguing.
On the other hand, some of the decision procedures extend to mild extensions
of first order logic as well. These logics have close connections to automata
theory and game theory.
The course is an attempt to survey some of the techniques used in this search
for decision procedures in this first order world.
1 Decidable fragments of FOL
quantifier prefix classes (syntactic restriction)
restricted classes of structures
arithmetics
variable confined logics (syntactic restriction)
guarded fragment (syntactic restriction)
2 Decidable extensions of FOL
counting quantifiers
fixed point quantifiers
MSO
References
The Classical Decision Problem, by E. Borger, E. Gradel and Y. Gurevich, Oct 2001, Springer.
Finite Model theory and its Applications, E. Gradel et al, 2007, Springer.
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Course 2:
Topics in games and logic
博弈与逻辑选讲
Credits: 2 points
3 hours/week, 10 weeks (April 8th - June 9th)
Classroom requirements: Blackboard+Beamer, 15 students
Assessment: presentation and reports
Synopsis:
Infinite games have been studied for long by set theorists and topologists,
mainly from the perspective of determinacy and descriptive complexity.
Alonzo Church suggested in 1953 that infinite games provided a good
framework for studying circuit synthesis, and the work of Buechi, McNaughton
and others in the 1960's and 70s developed on this idea. In the last two decades,
computer science has proceeded further looking into the complexity of
strategies. The study of multi-agent systems has also spurred interest in
the logical structure of such games and strategies in them. The course is
an attempt to understand these research trends.
infinite games & lack of determinacy
regular infinite games, memory-less determinacy for parity games
decidability of MSO on infinite words and infinite trees
mu-calculus
Game logic and its friends/descendants
Coalition logic
ATL & its variations
Research directions
References
Automata, Logic and infinite games, edited by Gradel, Thomas and Wilke, Springer LNCS 2500.
ESSLLI 2010 lecture notes on alternating temporal logics by Jamroga and Penczek.
ESSLLI 2011 lecture notes on reasoning about strategies by Ghosh and Ramanujam.