  In the last decades the logico-algebraic approach to quantum mechanics turned
to be a successful tool to render the quantum mechanical formalism on a steady
operationalistic background. The algebraic approach to general relativity first
proposed by Geroch is used to build a smearing procedure for events in the
quantized theory of spacetime. It stems from the notion of basic algebra which
possesses both the differential structure (as functional algebras) and
non-commutativity (as algebras of observables in quantum theories). The main
essence of this formalism is that it deprives the notion of spacetime as event
support of its fundamental status making it relative to the measurement
performed. Before the observation is executed, it is pointless to speak of
events as points of spacetime: there is no underlying manifold. Only when an
eigen-subalgebra of the basic algebra is outlined as eigenstate of the
observable, it gives rise to its functional representation on the appropriate
set thought of as spacetime.
