  Around 2000, J.-Y. Girard developed a logical theory, called Ludics. This
theory was a step in his program of Geometry of Interaction, the aim of which
being to account for the dynamics of logical proofs. In Ludics, objects called
designs keep only what is relevant for the cut elimination process, hence the
dynamics of a proof: a design is an abstraction of a formal proof. The notion
of behaviour is the counterpart in Ludics of the notion of type or the logical
notion of formula. Formally a behaviour is a closed set of designs. Our aim is
to explore the constructions of behaviours and to analyse their properties. In
this paper a design is viewed as a set of coherent paths. We recall or give
variants of properties concerning visitable paths, where a visitable path is a
path in a design or a set of designs that may be traversed by interaction with
a design of the orthogonal of the set. We are then able to answer the following
question: which properties should satisfy a set of paths for being exactly the
set of visitable paths of a behaviour? Such a set and its dual should be
prefix-closed, daimon-closed and satisfy two saturation properties. This allows
us to have a means for defining the whole set of visitable paths of a given set
of designs without closing it explicitly, that is without computing the
orthogonal of this set of designs. We finally apply all these results for
making explicit the structure of a behaviour generated by constants and
multiplicative/additive connectives. We end by proposing an oriented tensor for
which we give basic properties.
