This paper is the first attempt to learn the policy of an inquiry dialog system (IDS) by using deep reinforcement learning (DRL). Most IDS frameworks represent dialog states and dialog acts with logical formulae. In order to make learning inquiry dialog policies more effective, we introduce a logical formula embedding framework based on a recursive neural network. The results of experiments to evaluate the effect of 1) the DRL and 2) the logical formula embedding framework show that the combination of the two are as effective or even better than existing rule-based methods for inquiry dialog policies.