Date: Sept 8 (Sat), 2018

Venue: B114, Department of Philosophy, (李兆基人文学苑2号楼) Peking UniversitySpeakers:

Qinxiang Cao (SJTU)

Yanjun Li (Nankai)

Zachiri McKenzie (SJTU)

Kedian Mu (PKU)

Shengyang Zhong (PKU)

Yizheng Zhu (UCAS)

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### Program:

9:00 - 9:45 Qinxiang Cao:

*Unifying different separation logic semantics*

9:45 - 10:30 Yanjun Li:

*The Completeness for the Combination of PDL and EL with Perfect Recall and No Miracles*

tea break

11:00 - 11:45 Zachiri McKenzie:

*The Largest Initial Segment of a Model of Set Theory Point-wise Fixed by a Non-Trivial Automorphism*

11:45 - 12:30 Kedian Mu:

*Introduction to Inconsistency Measures and Their Properties*

lunch break

14:00 - 14:45 Shengyang Zhong:

*The Structure in a Hilbert Space: An Analysis via the Orthogonality Relation*

14:45 - 15:30 Yizheng Zhu:

*Projective Singletons*

tea break

16:00 - 17:30 Qinxiang Cao: Introduction to Coq

tea break

17:40 brainstorm

18:00 dinner

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### Abstracts:

*Unifying different separation logic semantics*

Qinxiang Cao (SJTU)

Results from so-called ``classical'' separation logics are not easily ported to so-called ``intuitionistic'' separation logics, and vice versa. Different separation logics have similar proof theories but their meta-theories were difficult to generalize. This limitation was due to their incompatible semantics. In this talk, I will introduce a unifying semantics and build a framework that allows to reason parametrically over all separation logics. This unifying semantics also reveals more connection between separation logics and (non-classical) modal logics.

*The Completeness for the Combination of PDL and EL with Perfect Recall and No Miracles*

Yanjun Li (Nankai)

We prove the completeness for the combination of propositional dynamic logic and single-agent epistemic logic in which the modalities interact. The kinds of interactions we consider are two commuting axioms, namely, the axiom of perfect recall and the axiom of no miracles. These two axioms capture the interactions between actions and knowledge.

*The Largest Initial Segment of a Model of Set Theory Pointwise Fixed by a Non-Trivial Automorphism*

Zachiri McKenzie (SJTU)

Abstract (PDF)

*Introduction to Inconsistency Measures and Their Properties*

Kedian Mu (PKU)

Inconsistency is one of the important issues in the community of knowledge representation and reasoning. Recently, measuring inconsistency has been considered as a necessary starting point to understand the nature of inconsistency in a knowledge base better. This talk will give a brief introduction to some typical inconsistency measures, as well as properties for characterizing ‘desirable’ measures in the framework of propositional logic.

*The Structure in a Hilbert Space: An Analysis via the Orthogonality Relation*

Shengyang Zhong (PKU)

Quantum theory relies heavily on the complicated mathematical theory of Hilbert spaces. Quantum logic, initiated by Birkhoff and von Neumann, is aimed at making clear the conceptual picture of quantum theory from a logical perspective and through in-depth study of the structure in Hilbert spaces. In this talk I will illustrate the research paradigm of quantum logic by my work in my PhD, i.e. an analysis of the orthogonality relation between the one-dimensional subspaces of a Hilbert space. I will also present my recent work on defining the orthogonality relation in the tensor product of two Hilbert spaces in terms of the orthogonality relations in the two components. This includes some nice facts about traces of linear maps. Future work in this direction may shed light on quantum entanglement, i.e. the intricate interactions between quantum systems which form one composite system.

Projective Singletons

*Yizheng Zhu (University of Chinese Academy of Sciences)*

$0^\#$ is a $\Pi^1_2$-singleton whose existence is a large cardinal assumption. Is there any $\Pi^1_2$-singleton whose L-degree is strictly in between 0 and $0^\#$? Friedman answered this question positively by class forcing over L. In this talk, we show how it generalizes to the higher even projective levels. We will describe the main difficulties and show how they are dealt with. This is joint work with Sy D. Friedman and Sandra Müller.

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### Organizers:

Zhaokuan Hao (Fudan)Yanjing Wang (PKU contact person)

Ruizhi Yang (Fudan)

Liang Yu (Nanjing)