The Delta Logic Workshops aim to bring logicians from Mathematics, Philosophy, and Computer Science together. The Delta 18 Logic Workshop will be held at Wuhan University.
Venue: B214, Zhenhua Building, School of Philosophy, Wuhan University, No.299 Bayi Road, Wuhan
Time: Saturday, February 25, 2023
Nan Fang (Institute of Software, Chinese Academy of Sciences)
Jixin Liu (Sichuan University)
Yinhe Peng (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
David Schrittesser (University of Toronto)
Ming Xiao (Nankai University)
Teng Zhang (Zhejiang University of Science and Technology)
Morning Session (Chair: Liuzhen Wu)
09:00–09:50 Nan Fang: Integer-valued martingales and cl-Turing reductions
Abstract: Integer-valued martingales are martingales which take values from integers. A real is called IVR if there is no integer-valued computable martingale succeeds on it. A cl-Turing reduction is a Turing reduction whose use function is bounded by some function n+c, where c is some constant. In this talk, we first show a correspondence lemma between them and thereby characterize IVR by cl-Turing reductions. Then we discover further properties of integer-valued martingales and show some related results. It is joint work with Lu Liu and Liang Yu.
09:50–10:40 Jixin Liu: Someone knows that local reasoning on hypergraphs is weakly aggregative
Abstract: This talk considers the following four topics: a class of generalized graphs whose relations do not have fixed arities called hypergraphs, a family of non-normal modal logics rejecting the aggregative axiom, an epistemic framework fighting logical omniscience, and the classical group knowledge modality of `someone knows'. Through neighborhood frames as their meeting point, we show that, among many completeness results obtained, the limit of a family of weakly aggregative logics is both exactly the modal logic of hypergraphs and also the epistemic logic of local reasoning with veracity and positive introspection, and upon adding a single combinatorial axiom, it is also the logic of `someone knows' for a fixed finite number of positively introspective agents. This is joint work with Yifeng Ding and Yanjing Wang.
10:40–11:10 Tea Break and Group Photo
11:10–12:00 Yinhe Peng: Applications of inner and outer approach in selection principles
Abstract: Approximating a set by an inner subset or an outer superset is a frequently used method in various fields. There are applications of inner approach in selection principles. However, they are mainly restricted to the CH assumption. In this talk, I will explore inner approach method in selection principles and discuss applications of inner approach under more general assumptions. The closely related outer approach will also be discussed.
12:00–14:30 Lunch Break
Afternoon Session (Chair: Haosui Duanmu)
14:30–15:20 David Schrittesser: Definability and madness
Abstract: Mathias asked whether ``every set is Ramsey'' implies ``there are no mad families''; a natural answer was given in 2019. In this talk, we discuss this and related results as well as subsequent generalizations to higher dimensional mad families.
15:20–16:10 Ming Xiao: Borel order dimension
Abstract: Order dimension is a classical combinatorial object introduced by Dushnik and Miller in 1941. We focus on Borel partial orders and analyse the order dimension that can be realized by Borel definable orders. This is joint work with Dilip Raghavan.
16:10–16:30 Tea Break
16:30–17:20 Teng Zhang: Additive and multiplicative structure on combinatorial notions
Guozhen Shen (Wuhan University)
Liang Yu (Nanjing University)
National Natural Science Foundation of China
School of Philosophy, Wuhan University