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In this paper we provide a brief overview of the two mathematical constructions presented by Yves Andr´e during the first two session of Ircam’s “Mathematical School for Musicians and other Non-Mathematicians”. After discussing a musical application of Operator Theory we try to suggest the possible connection between Jean-Yves Girard’s Geometry of Interaction (based on a special case of von Neumann algebras) and a recent topos-theoretical model of musical gesture [28] which provides an extension of the “classical” structure-oriented framework of Guerino Mazzola’s Topos of Music. This interpretation raises the question of the articulation between formal models, programming and computation in music and suggests some possible directions in the definition of “musical logic”.