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This paper presents a mathematical interpretation of the object-oriented modeling paradigm inspired from the Willems' behavioral approach of systems theory. The object modeling of interconnected dynamic systems is introduced independently from any computer language and expressed as a set computation problem. Two behavioral representations (complete and partial) of an object are defined. Three object relationships, i.e. instantiation, composition and generalization are examined in the behavioraldoi:10.1080/00207720601159803 fatcat:j73tmkdiwzgv3n3g5etwypy2bm