The notion of short sight, introduced by Grossi and Turrini, weakens the unrealistic assumption in traditional extensive games that every player is able to perceive the entire game structure. In this paper, we propose a more general model for extensive games with short sight. For reasoning about extensive games with short sight, we propose a new logic language and then present an axiomatization for this logic. We prove the soundness and completeness of the axiomatization. In addition, we show that the logic can formally characterize the solution concepts and Pearce's lemma in games with short sight.