This paper describes strategies for monitoring human behaviour within a smart home and, in a broader perspective, for context-assessment in cognitive systems. The proposed framework, which is inspired by a cognitive theory called Computational Functionalism, is aimed at integrating ontology and logic-based approaches to context representation and recognition. Two are the assumptions underlying the model: (1) the availability of an ontology (i.e., a “concept–role” representation of what is relevant in a given domain); (2) a simple inference scheme (i.e., subsumption between descriptions of elements within the ontology). The context model is formally defined adopting a structural approach that describes contexts and situations as hierarchical structures grounded with respect to the ontology. Examples are presented to discuss the proposed model.