Algebras of Measurements: the logical structure of Quantum Mechanics
Daniel Lehmann (Hebrew University)

Abstract: In Quantum Mechanics, a measurement gives not only a value
but also a new state of the system. Its logic is a logic in which
propositions act on states (models). We study the structure of the set
of such measurements as a set of operators on the states of the
system. This set of operators is not closed under
composition. Algebras of measurements are structures that abstract
from the set of all projections on closed subspaces of a Hilbert
space. Their defining properties are justified by epistemological
arguments. We study their properties, with special attention to
commutation of operators (i.e., projections). They define an order
structure that is not necessarily a lattice, but is orthomodular.

Co-authors: Kurt Engesser (Konstanz Un. and King's College, London)
and Dov M. Gabbay (King's College, London)