Time: 2024/03/12 15:10-18:00

Location: Room 313, Teaching Building No.2 (第二教学楼), Peking University

Speaker 1: Wen Tang

Title: Substitution as modalities

Abstract: Substitution is a crucial notion in logic, as often defined in the metalanguage in order to present and use the proof systems. In this talk, I will introduce systems that treat substitutions as dynamic modalities and thus making them first-class citizens in the object language. Inspired by the reduction axioms in public announcement logic and epistemic logic with assignments, we obtain complete axiomatizations of basic propositional logic, modal logic, and first-order logic with the relevant substitution operators, such that the formal systems do not need to refer to the metalanguage notion of substitution anymore. And I will discuss some interesting properties of substitution operators in this talk.

Speaker 2: Qianli Ma

Title: 关于学习理论的动态逻辑

Abstract: 本次报告主要基于A. Baltag, N. Gierasimczuk等于2019年发表的工作A dynamic logic for learning theory。形式学习理论对归纳学习的过程作出了一个比较开放与宽松的刻画。结合动态知识逻辑与拓扑子集语义，以及从拓扑角度对形式学习理论的研究，可以构造出一个可靠且完全的DLLT系统（dynamic logic for learning theory）。在这个系统的刻画中，信念将被理解为学习者作出的假设，而可以通过归纳学习到的知识将被理解为不会被否决的信念。