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ArchiTRIO [14] is a formal language, which complements UML 2.0 concepts with a formal, logic-based notation that allows users to state system-wide properties, both static and dynamic, including real-time constraints. In this paper we present the semantics of the core concepts of the ArchiTRIO language. As the core elements of ArchiTRIO coincide with those of UML 2.0 (operation, interface, port, class), the semantics of ArchiTRIO provides also a formal definition for the basic concepts on which UML 2.0 is built.