This paper provides a linguistic semantic analysis of time and aspect in natural languages. On the basis of topological concepts, notions are introduced like the basic aspectual opposition between event, state and process or that of time of utterance (for the treatment of deictic categories) that are used to analyse the semantics of grammatical tenses or more general situations. This linguistic model yields a conceptualisation reused for the definition of a formal ontology of time and aspect. This ontology is provided with a formal framework based on type theory that enables the processing of temporal and aspectual semantic entities and relations.