Dialogue Understanding in a Logic of Action and Belief

In recent work, Langley et al. (2014) introduced UMBRA, a system for plan and dialogue understanding. The program applies a form of abductive inference to generate explanations incrementally from relational descriptions of observed behavior and knowledge in the form of rules. Although UMBRA’s creators described the system architecture, knowledge, and inferences, along with experimental studies of its operation, they did not provide a formalization of its structures or processes. In this paper, we analyze both aspects of the architecture in terms of the Situation Calculus—a classical logic for reasoning about dynamical systems—and give a specification of the inference task the system performs. After this, we state some properties of this formalization that are desirable for the task of incremental dialogue understanding. We conclude by discussing related work and describing our plans for additional research.