Update Semantics for Imperatives with Priorities Fengkui Ju 1⋆⋆ and Fenrong Liu 2 1 Department of Philosophy, Beijing Normal University, Beijing, China jufengkui@gmail.com 2 Department of Philosophy, Tsinghua University, Beijing, China fenrong@tsinghua.edu.cn Abstract. Imperatives occur ubiquitously in our social communications. In real life we often get conflicting orders issued by different speakers whose authorities are ranked. We propose a new update semantics to interpret the meaning of imperatives with priorities and illustrate what changes they bring about in the addressee’s cognitive state. The general properties of the semantics, as well as its core philosophical ideas are discussed extensively in this paper. Keywords: imperatives, conflicts, update semantics, priorities 1 Introduction Imperatives occur ubiquitously in our social communications. To act successfully in a society, we have to fully understand their meaning, as imperatives regulate actions. Logical studies on imperatives have been carried out for some time, and deontic logics belong to such a tradition. From the 1990s, several prominent new frameworks have been proposed. Following the slogan “you know the meaning of a sentence if you know the change it brings about in the cognitive state of anyone who wants to incorporate the information conveyed by it”, update semantics ([9]) was proposed to deal with information update, and it was later applied to imperatives in [8], [6] and [10]. On the basis of deontic logics, [1] made a proposal to study actions that are typically expressed by STIT-sentences “see to it that...”, bringing actions with choices made by agents together. Other recent works in this line are [4], [2] and [3]. Adopting dynamic epistemic logic (DEL) approach, [11] and [12] introduced a new dynamic action of “commanding” to deontic logic, and dealt with imperatives in the framework of dynamic deontic logics. So far, the main purpose of those approaches has been to understand the meaning of one single imperative. Not much attention has been paid to conflicting orders, which were simply taken to be absurd, thus resulting very trivial facts in the existing frameworks. In addition, though agency was introduced to the research agenda, the focus has been always on the addressee, not on the addressors. However, in ⋆⋆ The order of the authors’ names is alphabetical, and both authors contributed equally to this work.