- 逻辑学基础理论 (Foundations of logic)
The course gives an overview of classical meta-logical results, in particular, Godel’s completeness and incompleteness theorems, Church-Turing’s proof of the undecidability of rst-order logic, and Tarski’s theorem on the undenability of truth. After a recapitulation of the syntax and semantics of first-order logic, Henkin’s proof of completeness, in terms of syntactic models and maximal consistent sets, is presented. Philosophical and logical consequences of the result and its proof are discussed, with some glimpses from model theory. The course then presents the notions of complete and incomplete theories, as well as decidability of theories. After an overview of the philosophical and mathematical background in the early 20th century, including Hilbert’s Program, the incompleteness theorems and related results, and the ideas behind their proofs, are presented at an informal level. The remainder of the course lls in some of the details. The course presentation focuses on important concepts and ideas, philosophical as well as mathematical, but also gives pointers to the technical details.
- 模态逻辑及其应用 (Modal logic and its applications)
Among branches of modern logic, modal logic provides a nice balance of expressivity and complexity, allowing it to be applied widely and extensively in many fields ranging from humanities to software design. In this course, ideas and methods of modal logic will be introduced along with its famous applications in modeling time, knowledge, necessity, and social behaviors. In this thread, student will be led into enviroments similar to research, in which ideas and needs from theoretical side and practical side frequently interact. Pointers will be given to standard textbooks/handbooks as well as notable papers, and with knowledges and skills introduced in this course, students with further interests should in principle be able to explore by their own. This course aims to student who more or less have learnt some logic, but this is not strictly required.
- 模型论 (Model theory)
Introduction to model theory as a capacity training, following Hodges’ Shorter textbook.
- 弗雷格的语言哲学 (Frege’s Philosophy of Language)
Gottlob Frege is one of the milestones in the history of the western philosophy, even though his name is almost unknown to the non-philosophical public. He is the inventor of the modern logic. At the same time, his works concerning the nature of arithmetic give birth to a tradition within the philosophy of mathematics that is called “logicism”. Furthermore, just in his “leisure time”, he has managed to be the father of the modern philosophy of language. Without him, the philosophical landscape nowadays would take a totally different shape. In this course, we will try to get insight into his philosophy of language. More precisely, we are going to focus on two topics. The first one is Frege’s semantic theory concerning those sentences which contain at least one name that lacks reference. Based upon a careful study of Frege’s own writings, we will compare his view with some theoretical options offered by other philosophers like Russell and Strawson. The second topic is Frege’s redundancy theory concerning the concept of truth that is quite interesting on the one hand and exhibits some internal tensions on the other hand.
- 一阶逻辑 (First-order logic)
From very beginning to the completeness theorem (countable language), step by step and seriously.
- 人工智能中的逻辑 (Logic in AI)
This is a seminar style course. We aim to present recent research in logic that interacts with philosophy, linguistics, social sciences, computer science and AI. Our first topic is the meaning of logical constants in various logics, how that meaning is related to logical consequence, and what this says about the nature of logic. Next we consider how generalizations, and in particular generalizations with exceptions, are expressed in natural languages, using tools from generalized quantifier theory. We go on to investigate a few logics and formal models that have been used to study some intriguing phenomena in social networks. Simulations will be presented to illustrate the properties of social networks. We will invite some guests whose research is relevant to the seminar topics to present their latest ideas. Students are required to read relevant papers and present part of papers in class, at the end they need to hand in a final paper in English 10-15 pages.
- 逻辑与知识论 (Logic and epistemology)
This course is an introduction to epistemology: the theory of knowledge. We will explore the history of various issues of epistemology, with a focus on the notion of knowledge, the relationship between knowledge, belief and evidence. In addition, we will pay particular attention on skepticism, namely, the thesis that we know nothing at all—and we will survey a range of skeptical arguments and responses to skepticism. In addition we will also look at the issues considered in some new branches, for instance, formal epistemology and social epistemology.
- 逻辑、语言与哲学 (Logic, language and philosophy)
This course is designed for students with backgrounds and interests in philosophy, and consists of two parts. The first part of the course introduces fundamental logical notions and methods that have applications in philosophy. Things to be covered include logical systems like propositional logic, predicate logic, epistemic logic, and dynamic logic, as well as issues like inter-translation of formal and natural languages, inference pattern and calculus, epistemic activity and information flow, and the interaction between logic and games. The second part of the course introduces the students to the application of logic in the study of natural language semantics. It gives an overview of the main tools and theoretical approaches, provides concrete examples of a number of phenomena, and discusses both historical backgrounds as well as some methodological assumptions.
- 哲学逻辑 (Philosophical logic)
This course is a research seminar for graduate students and advanced undergraduates. We will introduce several research areas, with a focus on the current research topics. Whenever necessary, we will invite colleagues from other universities to present their work. The students are required to read the relevant literature. We hope to bring the students to the research front, so that they can find a topic of their interest. Topics include: Game logics (logical analysis of game structures / logical analysis of players and play / logic, games, and computation / logic as games and gamification); Logics for social networks (belief revision in social networks / epistemic logic of friendship / modelling communication in social networks / social structures and simulations); Theories of truth, rationality and logic (the problem of defining truth / truth, meaning and interpretation / truth and action explanation / truth and the foundations of logic).