In human-human conversations, listeners often convey intentions to speakers through feedback consisting of reflexive short responses. The speakers recognize these intentions and change the conversational plans to make communication more efficient. These functions are expected to be effective in human-system conversations also; however, there is only a few systems using these functions or a research corpus including such functions. We created a corpus that consists of users' short responses to an actual conversation system and developed a model for recognizing the intention of these responses. First, we categorized the intention of feedback that affects the progress of conversations. We then collected 15604 short responses of users from 2060 conversation sessions using our news-delivery conversation system. Twelve annotators labeled each utterance based on intention through a listening test. We then designed our deep-neural-network-based intention recognition model using the collected data. We found that feedback in the form of questions, which is the most frequently occurring expression, was correctly recognized and contributed to the efficiency of the conversation system.