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In [7] the authors of this paper argued in favor of the possibility toconsider a Paraconsistent Approach to Quantum Superpositions (PAQS). We claimedthat, even though most interpretations of quantum mechanics (QM) attempt toescape contradictions, there are many hints -coming from present technical andexperimental developments in QM- that indicate it could be worth while toengage in a research of this kind. Recently, Arenhart and Krause have raisedseveral arguments against the PAQS [1, 2, 3]. In [11, 12] it was argued thattheir reasoning presupposes a metaphysical stance according to which thephysical representation of reality must be exclusively considered in terms ofthe equation: Actuality = Reality. However, from a different metaphysicalstandpoint their problems disappear. It was also argued that, if we accept theidea that quantum superpositions exist in a (contradictory) potential realm, itmakes perfect sense to develop QM in terms of a paraconsistent approach andclaim that quantum superpositions are contradictory, contextual existents.Following these ideas, and taking as a standpoint an interpretation in terms ofthe physical notions of power and potentia put forward in [10, 12, 15], wepresent a paraconsistent formalization of quantum superpositions that attemptsto capture the main features of QM.

The Paraconsistent Approach to Quantum Superpositions Reloaded: Formalizing Contradictory Powers in the Potential Realm