  To help resolve stubborn aporias in quantum mechanics, Kastner, Kauffman and
Epperson have recently proposed a new interpretation of Heisenbergs ontological
duality of res extensa and res potentia. In related work, Khrennikov and Aerts
and their respective associates have explored the intermediate domain of
mesoscopic phenomena in which quantum-like behavior can be observed and
formalized. We generalize this work to define a third domain, one of
macroscopic, interactive processes to which quantum concepts, but not quantum
formalism apply. We show that they follow the non-standard logic proposed in
the last century by the FrancoRomanian thinker Stephane Lupasco. This logical
system, grounded in the ontological dualities in nature, describes the
evolution of complex processes and emergence at macroscopic levels of reality
as chains of interacting actualities and potentialities. Without going outside
the laws of physics, some new approaches to the problems of life, cognition and
information can be made. The most appropriate formalism for describing this
logic is under current scrutiny.
