Speaker: Chenwei Shi (Department of Philosophy, Tsinghua University, Beijing)
Date and Time: Thursday, May 28th 2020, 16:30-18:00, Amsterdam time.
Title: Logic of Convex Order (Joint work with Yang Sun)
Abstract. Given a preference order on a set of possible worlds, there are different ways of extending/lifting it to a preference order on sets of worlds. For example, A >= B if and only if for all elements b in B there is an element a in A such that a >= b. This way of lifting order is usually named after Lewis, called l-lifting. In this talk, I will focus on another well-known way of order lifting, called “Egli-Milner ordering”. Compared with the l-lifting, it only adds one more condition: for all elements a in A there is an element b in B such that a >= b. In this talk, I will examine the resulting logic of the Egli-Milner order. By presenting a sound and complete axiom system, I will show that the Egli-Milner order is “convex”, which can be seen as a weaker form of monotonicity. To further illustrate the non-monotonicity of the Egli-Milner order, I will then discuss the relation between l-lifting, Egli-Milner order and conditional belief defined in a plausibility model.