Symmetry in sequent calculus and Matte Blanco´s bi-logic

We discuss the problem of symmetry, namely of the orientation of the logical consequence, represented by the sequent sign in sequent calculus. We show that the problem is surprisingly entangled with the problem of “being infinite”. We present a model based on quantum states and we show that the requirements of Matte Blanco´s symmetric mode are satisfied. We briefly discuss the model for symmetry to include correlations, in order to obtain a possible approach to displacement. In this setting, we find a possible reading of the structural rules of sequent calculus, whose role in computation, on one side, and in the representation of human reasoning, on the other, has been debated for a long time.