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### Abstract

Anhomomorphic logic, is a novel interpretation of Quantum Theory (initiated
by Sorkin) that comes as a development of the consistent histories approach and
is an attempt to retain realism. When using logic to describe (classical)
physics, we have a set of possible histories, a set of truth values ( e.g.
{True, False}) and the possible maps (Phi_i) that are homomorphisms between the
Boolean algebra of subsets of and of the truth values. These maps give rise to
different realizations (here is where the measure and thus the dynamics enter
the picture).
It is well known that the above picture cannot hold in quantum theory. One can
either restrict the subsets of allowed (standard consistent histories) or
change
the set of truth values to some Heyting algebra (Isham) or finally, weaken the
requirement that the map is homomorphism. This latter approach is taken in
"Anhomomorphic Logic". The weakening of the requirement to be a
homomorphism
is replaced by other conditions, that guarantee that most structure is
preserved and the basic inference law (modus ponens) still aplies. Thus we have
a deductive logic (which is not the case in what is usually referred to as
"quantum logic"). In this talk, we will first introduce anhomomorphic
logic in
some
detail. Then we will deal with some recent developments on the emergence of
classicality and the closely related issue of recovery of probabilistic
predictions.
The former, essentially means that in some scale of coarse graining, we know
that
classical (boolean) logic applies. Thus we have to show that the anhomomorphic
logic, upon some coarse grainings, results to homomorphic logic (i.e.
classical).
Finally, the issues of how probabilities arise, is present in several attempts
to
retain realism in quantum theory (such as many worlds), and in this approach
it is resolved with the use of the concept of "approximate
preclusion" and by
taking a frequentist's view on probability rather than treating it as
propensity.