Quantum logic and applied categories

Quantum logic and applied categories

[M Heather]

	The complexity of the contributions on this subject seem unlikely to
encourage applicable category theory. Quantum Logic is perhaps a prime
example where CT can deal directly with 'non-locality' without recourse to
quasi-linear reductions like the non-distributive orthocomplemented modular
lattice. That may be the accepted interpretation but not for its scientific
merits more from an argument ad hominem as it arose from a particular
thought experiment of von Neumann.
	QL in CT via Hilbert spaces is to model a model. A stream can never
rise higher than its first spring, said Francis Bacon at the outset of
modern science.  Surely QL is much better represented by the higher internal
logic of a general topos as it satisfies the correspondence principle. The
non-distributive lattice version on the other hand cannot.
	The papers
<http://computing.unn.ac.uk/staff/CGNR1/liege_quantum02.pdf>
	<http://computing.unn.ac.uk/staff/CGNR1/liege_quantum03.pdf>
	discuss for a BCS Cybernetic Machine Group publication how CT can
subsume the various interpretations to help achieve quantum computation in
natural computing. These draw on the neutral concept of the anticipatory
system introduced by Rosen who has advocated the use of CT for representing
life systems.
	Quantum logic is in a class of modern 'non-local' problems like
natural language, information theory, globalisation, social systems, etc
that could be greatly advanced by the use of applied category theory.
Unfortunately there appears to be no readily available treatise on CT that
is not heavily couched in  'local' set-like language and able to pass the
adequacy test of Bacon.
	Michael Heather