  We present a general formalism with the aim of describing the situation of an
entity, how it is, how it reacts to experiments, how we can make statistics
with it, and how it changes under the influence of the rest of the universe.
Therefore we base our formalism on the following basic notions: (1) the states
of the entity; they describe the modes of being of the entity, (2) the
experiments that can be performed on the entity; they describe how we act upon
and collect knowledge about the entity, (3) the probabilities; they describe
our repeated experiments and the statistics of these repeated experiments, (4)
the symmetries; they describe the interactions of the entity with the external
world without being experimented upon. Starting from these basic notions we
formulate the necessary derived notions: mixed states, mixed experiments and
events, an eigen closure structure describing the properties of the entity, an
ortho closure structure introducing an orthocomplementation, outcome
determination, experiment determination, state determination and atomicity
giving rise to some of the topological separation axioms for the closures. We
define the notion of sub entity in a general way and identify the morphisms of
our structure. We study specific examples in detail in the light of this
formalism: a classical deterministic entity and a quantum entity described by
the standard quantum mechanical formalism. We present a possible solution to
the problem of the description of sub entities within the standard quantum
mechanical procedure using the tensor product of the Hilbert spaces, by
introducing a new completed quantum mechanics in Hilbert space, were new 'pure'
states are introduced, not represented by rays of the Hilbert space.
