Public screens are common in modern society, and provide information services to audiences. However, as more and more screens are installed, it becomes a burden for users to find information concerning themselves quickly. This is because screens cannot understand what users really need, they only display pre-designed information related to a certain location. To ensure better cohabitation between people and screens, one solution is to make screens understand users rather than make users understand screens. Given that it is difficult, even for humans, to interpret other people's intentions, it is far harder for screens to understand users. We need first to decide which kinds of information about users could be helpful for a screen to estimate to users' needs. In this paper, we study a public interactive screen, which can speculate as to users' intentions by interpreting their proxemic attributes (such as dis- tance, movement, etc.) and context information (identity, locations, etc.). Based on proxemic interaction semantics, we built an interactive pub- lic screen, which: 1) could interpret users' needs in advance and display relevant information; 2) be available for multi-users and display distinct information to them; 3) be open for data exchanges with users' mobile devices. Through a lab study, we demonstrate that the screen presented in this paper is more attractive to users and could provide users with useful information more rapidly and precisely than traditional screens.