  We define and construct a new data structure, the tables, this structure
generalizes the (finite) $k$-sets sets of Eilenberg \cite{Ei}, it is versatile
(one can vary the letters, the words and the coefficients). We derive from this
structure a new semiring (with several semiring structures) which can be
applied to the needs of automatic processing multi-agents behaviour problems.
The purpose of this account/paper is to present also the basic elements of this
new structures from a combinatorial point of view. These structures present a
bunch of properties. They will be endowed with several laws namely : Sum,
Hadamard product, Cauchy product, Fuzzy operations (min, max, complemented
product) Two groups of applications are presented. The first group is linked to
the process of "forgetting" information in the tables. The second, linked to
multi-agent systems, is announced by showing a methodology to manage emergent
organization from individual behaviour models.

Multiagent Systems;Discrete Mathematics