Initiated by the center’s students and researchers in 2019, the Tsinghua Logic Salon has quickly grown into a lively platform for try-outs and exchanges of new ideas. Researchers in various fields of logic are invited to present their latest research, as well as the challenges that they see. Every participant is encouraged to engage in discussions and exchange of perspectives. Each session lasts for 1.5 hours in total, with 30 minutes of discussion included.

Organizing Committee (from September 2023): Junhua Yu, Chenwei Shi, Wei Wang, Jialiang Yan, Penghao Du.

### ■Schedule for 2023-2024 academic year

Date | Speaker |
---|---|

2024 FEB 29 | 张俊 ZHANG Jun |

2024 MAR 14 | Byeong-uk Yi |

2024 MAR 21 | 贺飞 HE Fei |

2024 MAR 28 | Wes Holliday |

2024 Apr 18 | 张长水 ZHANG Changshui |

2024 MAY 09 | 高速 |

2024 MAY 23 | 徐源 |

### ■Current Events

**2024 May 09 16:00-17:00 Su Gao (高速, Nankai University) Universal Structures in Continuous Logic**

Continuous logic is a nonstandard multi-valued logic developed in recent years to study metric structures. In this talk we consider the question whether universal structures with the Urysohn property exist in continuous logic. It turns out that the answer depends on some particular properties of the continuous signatures. In this talk I will give conditions that will completely characterize the existence of Urysohn structures and some other related properties in continuous logic. This is joint work with Xuanzhi Ren.

**2024 Apr 18 16:00-17:30 Changshui Zhang (Tsinghua University) 学习与推理**

推理是传统人工智能中的重要研究方向，取得了很多成果。机器学习是当前人工智能研究的重要方向，特别是深度学习方法展现出强大的学习能力。在这个报告中，我们从一些实际应用问题开始，讨论学习和推理结合的实际需求，探讨这一研究方向的不同解决思路和关键问题。

**2024 Mar 28 16:00-17:30 Wesley H. Holliday (University of California, Berkeley) Preconditionals**

Conditionals in their different flavors—material, strict, indicative, counterfactual, probabilistic, constructive, quantum, etc.—have long been of central interest in philosophical logic. In this talk, we will discuss our recent work on a new semantics for conditionals, covering a large class of what we call preconditionals. Familiar examples of bounded lattices equipped with a preconditional include Heyting algebras, ortholattices with the Sasaki hook, and Lewis-Stalnaker-style conditional algebras satisfying the so-called Flattening axiom. We have shown that every bounded lattice equipped with a preconditional can be represented using a relational structure (suitably topologized), yielding a single relational semantics for conditional logics normally treated by different semantics, as well as generalizing beyond those semantics. An associated paper is available at https://arxiv.org/abs/2402.02296.

#### 2024 Mar 21 16:00-17:30 贺飞（清华大学） 面向并发程序的逻辑理论及其自动判定工具

逻辑是刻画程序语义的基础。可满足性模理论（SMT）求解器是许多程序分析与验证技术的推理引擎。目前，存在多种一阶理论，例如线性算术理论、数组理论、位向量理论、未解释函数理论等，基于这些理论已经能够很好的支持串行程序验证。然而，却缺乏直接面向并发程序验证的一阶理论。本报告介绍我们在并发程序逻辑理论方面取得的最新研究成果，并介绍相应的自动判定算法和程序验证工具。基于该理论开发的并发程序验证工具Deagle连续三年获得国际软件验证大赛并发安全赛道冠军。

#### 2024 Mar 14 16:00-17.30 Byeong-Uk Yi (University of Toronto) *Is Logic Axiomatizable?*

I defend the negative answer to the question in the title, “Is logic aziomatizable?”, by considering sentences that involve plural constructions, such as the following:

[A] There are some things each of which admires one of them.

[B] There are some critics who admire only one another.

We can intuitively see that [A], for example, is logically implied by infinitely many sentences, such as the following:

[A1] c1 admires c2.

[A2] c2 admires c3.

…

[An] cn admires cn+1.

…

But [A] is not logically implied by any finite number of sentences among these. So the logic of languages that are rich enough to include [A] is non-compact. It follows from this that the logic of such languages is not axiomatizable. Similarly, we can see that [B], known as the Geach-Kaplan sentence, is logically implied by the following sentences (but not by any finite number of them):

[A1] c1 admires only c2, c1 is not c2, and c1 is a critic.

[A2] c2 admires only c3, c2 is not c3, and c2 is a critic.

…

[An] cn admires only cn+1, cn is not cn+1, and cn is a critic.

…

So we can conclude that the logic of languages that include [B] is not axiomatizable.

To put the argument in proper perspective, I shall discuss contemporary account of plural constructions and suggest that they fail to do justice to the logic of plural constructions because they are based on the traditional view of plural constructions as devices for abbreviating singular constructions. And I shall give a sketch of my account of the logic of plural constructions that are based on the view of plurals as substantial devices that complement their singular cousins.

#### 2024 Feb 29 16:00-17.30 Jun Zhang (University of Michigan Ann Arbor & Shanghai Institute for Mathematics and Interdisciplinary Sciences) *Cognitive Core of Mathematical Reasoning: Some Thoughts*

My talk will explore a common foundation for mathematical reasoning and for their underlying cognitive processes. Starting from counting and spatial reasoning as two core developmental domains of mathematical cognition, I will discuss how the notion of object can be characterized by “concept lattice” (as in Formal Concept Analysis of Ganter and Wille 1999), and how the structure of knowledge can be captured by “knowledge space” (and its learning space, by Doignon and Falmagne 2015). Finally, motivated by the intertwined relations among lattice, logic, and topology, I will describe how the suite of topological operators, and hence topological semantics, can be generalized to general set systems (Lei and Zhang 2019), paving the way for using the latter as the common core for mathematical/formal cognitive systems.

### ■Past Events

Click HERE to check the past events.