Title: Exploring instantial operators for neighborhood structures

Speaker: Junhua Yu (Department of Philosophy, Tsinghua University)

Place: Room B114, Lee Shau Kee Humanities Buildings No. 2

Time: 15:10-18:00, Dec. 8th (Friday)

Abstract: A neighborhood frame is an ordered pair of a non-empty set W and a `neighborhood function' that maps each point in W to a collection of subsets of W (each subset is called a `neighborhood' of that point). A neighborhood model is a neighborhood frame whose points are propositionally valuated. In the field of modal/philosophical logic, neighborhood structures are usually employed as tools to induce non-normal weak logics in some basic modal languages (propositional languages with unary modal operators). A new era was initiated by van Benthem et.al.'s 2017 work that introduces an (more expressive) `instantial' operator. The instantial operator is (j;1)-ary, and a formula like [](A1,...,Aj;A0) means the current point has a neighborhood in which A0 is universally satisfied and none of A1,...,Aj (each is called an `instance') is universally falsified. After recalling preliminaries, we will present our study on variants of the instantial operator. We will talk about instantial operators that have a limited number of instances, that require instances to be satisfied on pairwise distinct points, and that have generalized quantifier entries. This talk is based on joint works with Han Gao, Dazhu Li, Chen Wang, and Yichen Zhao.