Dialogue‐based systems often consist of several components, such as communication analysis, dialogue management, domain reasoning, and language generation. In this paper, we present Converness, an ontology‐driven, rule‐based framework to facilitate domain reasoning for conversational awareness in multimodal dialogue‐based agents. Converness uses Web Ontology Language 2 (OWL 2) ontologies to capture and combine the conversational modalities of the domain, for example, deictic gestures and spoken utterances, fuelling conversational topic understanding, and interpretation using description logics and rules. At the same time, defeasible rules are used to couple domain and user‐centred knowledge to further assist the interaction with end users, facilitating advanced conflict resolution and personalised context disambiguation. We illustrate the capabilities of the framework through its integration into a multimodal dialogue‐based agent that serves as an intelligent interface between users (elderly, caregivers, and health experts) and an ambient assistive living platform in real home settings.