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LFCS seminar by Prof. Philip Scott (U. Ottawa, Canada)

MV Algebras, Effect Algebras, and Inverse Semigroups

What
When May 15, 2014
from 02:00 PM to 03:00 PM
Where IF G.07A
Contact Name Alex Simpson
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MV algebras are the algebras associated with certain many-valued logics,
developed by Lukasiewicz and the Polish logic school in the 1920's. They
were first studied mathematically in the 1950's by the model theorist
C.C. Chang and also by R. McNaughton. They are related to both
probabilistic as well as "fuzzy" logics.  In the 1980's, the logician D.
Mundici found deep mathematical connections of MV algebras with
important classification theory of C*-algebras in functional analysis,
as well as connections with certain algebras used in mathematical
physics.  In a somewhat different direction, in the 1990's, physicists
studying the theory of "quantum effects" and "unsharp measurement" in
quantum-mechanical systems developed "quantum effect algebras", which we
now know are intimately related to MV algebras.  More recently, through
work with Mark Lawson (Heriot-Watt), we see connections of MV algebras
with inverse semigroups related to non-commutative Stone Duality,
topological groupoids, prefix codes, and tiling theory.

In this talk I will introduce MV algebras, some of their associated logics, as well as
recent work on coordinatizing MV-algebras (joint work with Mark Lawson).

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