The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations. (arXiv:1801.00446v1 [quant-ph])

In this paper we present a new categorical approach which attempts to provide
an original understanding of QM. Our logos categorical approach attempts to
consider the main features of the quantum formalism as the standpoint to
develop a conceptual representation that explains what the theory is really
talking about --rather than as problems that need to be bypassed in order to
allow a restoration of a classical "common sense" understanding of what there
is. In particular, we discuss a solution to Kochen-Specker contextuality
through the generalization of the meaning of global valuation. This idea has
been already addressed by the so called topos approach to QM --originally
proposed by Isham, Butterfield and D\"oring-- in terms of sieve-valued
valuations. The logos approach to QM presents a different solution in terms of
the notion of intensive valuation. This new solution stresses an ontological
(rather than epistemic) reading of the quantum formalism and the need to
restore an objective (rather than classical) conceptual representation and
understanding of quantum physical reality.

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