This thesis describes the theory and implementation of a semantic analyser and a dialogue modeller for the AthosMail application, a telephonic e-mail client. The hypothesis of this research is that dialogue in an interactive system can be managed by reasoning from a model grown as the dialogue progresses by interpreting in the current context a formal representation (logical form) of the latest utterance. Each logical form is derived context-independently using property theory (a highly expressive logic) and constitutes a single linguistic act (to the exclusion of speech acts). In this demonstration of the concept, the components are based on the Parasite system and implemented as separate agents in the agent-oriented Athos architecture used for the application. Each is written principally in Prolog with a Java wrapper that provides interaction with the rest of the software. The semantic analysis agent processes the output of Connexor's functional dependency parser for English and Swedish utterances and produces an unanchored logical form using a system of compositional semantics based on property theory. The dialogue modeller anchors and skolemizes this logical form, then uses an inference engine to determine the user's goal and to solve any necessary queries, while maintaining a structured model of the human-computer dialogue as it progresses. The goal and list of solutions are processed by another agent, the response planner, which takes additional information (such as the user's preferences) into account and specifies the actions to be taken by other agents, e.g. utterances to be generated and played to the user and alterations to the mailbox (such as deleting messages or marking them as read).