  In a recent paper, the author introduced an operational description of
physical theories where probabilities are replaced by counterfactual statements
belonging to a three-valued (i.e. possibilistic) semantic domain. The complete
axiomatic of these Generalized possibilistic Theories is generalized and
clarified in the present paper. The problem of bipartite experiments is then
addressed as the main skill of this paper. An axiomatic for the tensor product
of our spaces of states is given and different solutions are explicitly
constructed. This description of tensor products of Inf semi-lattices is partly
independent from the usual mathematical description of this problem. The nature
of the tensor product of orthocomplemented Inf semi-lattices is then also
explored. This subject is indeed fundamental for the development of a
reconstruction program for quantum theory within our framework. Our analysis
constitutes a first step towards this achievement.
