Positive nested conceptual graphs

This paper deals with positive (i.e. without negation) nested conceptual graphs (NCGs). We first give a general framework-graphs of graphs provided with morphism-for defining classes of NCGs. Then we define a new class of NCGs-typed NCGs- and we show that known kinds of NCGs can be described very simply as classes of the general framework. All NCG models considered generalize the simple CG model in the sense that they involve objects which are generalizations of simple CGs and reasonings on these objects are based on a graph operation (projection) which is a generalization of that used for simple CGs. Furthermore, the general framework introduced allows one to consider all these models as slight variations of a unique notion. This study has been initiated by applications we are currently involved in.