In a multimodal human-machine conversation, user inputs are often abbreviated or imprecise. Simply fusing multimodal inputs together may not be sufficient to derive a complete understanding of the inputs. Aiming to handle a wide variety of multimodal inputs, we are building a context-based multimodal interpretation framework called MIND (Multimodal Interpreter for Natural Dialog). MIND is unique in its use of a variety of contexts, such as domain context and conversation context, to enhance multimodal interpretation. In this chapter, we first describe a fine-grained semantic representation that captures salient information from user inputs and the overall conversation, and then present a context-based interpretation approach that enables MIND to reach a full understanding of user inputs, including those abbreviated or imprecise ones.