This paper presents a framework for temporal representation and reasoning in the MUSING project (http://www.musing-project.eu) which is dedicated to the investigation of semantic-based business intelligence solutions. Temporal information is based on a diachronic representation of time. Since ontological knowledge in MUSING is encoded in OWL, extending binary relations with time is not that easy, due to the fact that OWL (or description logic in general) only provides unary and binary relations. To do so, we need the notion of a time slice. Contrary to Welty et al., we directly interpret the original entities as time slices in order to avoid a duplication of the original ontology and to prevent a knowledge engineer from ontology rewriting. We will see that this reinterpretation makes it easy to extend an arbitrary upper/domain ontology with the concept of time. The diachronic representation of time is complemented by a sophisticated time ontology that supports underspecification and an arbitrarily fine granularity of time. MUSING makes use of a general upper-base ontology called PROTON (http://proton.semanticweb.org) that has been extended mostly by the MUSING partners from DERI, Innsbruck. We describe how the time ontology has been interfaced with PROTON and how it can be interfaced with OWL-Time. In the last third of this paper, we explain our choices that have led to a specific reasoning architecture in MUSING, based on Pellet, OWLIM, and Jena, and backed up by Sesame.