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# Conceptual Graphs

The theory of conceptual graphs (CG) has been developed to model the semantics of natural language (see [8]). Specifications based on conceptual graphs are therefore intuitive in the sense that there is a close relationship to the way human beings represent and organize their knowledge. From a mathematical point of view a conceptual graph is a finite, connected, directed, bipartite graph. The nodes of the graph are either concept or relation nodes. Due to the bipartite nature of the graphs, two concept nodes may only be connected via a relation node. A concept node represents either a concrete or an abstract object in the world of discourse whereas a relation nodes defines a context between two or more concepts.

Figure 6.1: A simple conceptual graph with two concepts and one relation.

A sample CG is depicted in figure 6.1. This CG consists of two concepts (white nodes) and one relation (black node). This CG expresses the fact that a printer is a hardware device. The two concepts -- `PRINTER` and `HARDWARE-DEVICE` -- are placed in a semantical context via the binary relation `IS-A`. The theory of CGs defines a mapping from conceptual graphs to first-order calculus. This mapping, which is described in [8], would map the CG depicted in figure 6.1 to the first order formula . As can be seen, the variables x and y form the link between the two concepts via the predicate `IS-A`.

Given a conceptual and relational catalogue, one can express arbitrary knowledge. For this reason the theory of CG represents a knowledge representation technique. The work done in [8] focuses on the representation of natural language. We have shown, that with a suitable conceptual and relational catalogue one can translate operational interface specifications to conceptual graphs (see [6]). We have written translators which translate arbitrary DCE and CORBA-IDL specifications to CGs. Thus we have already demonstrated that an implementation of an interface repository, which is based on such a meta-notation, can be used in different middleware platforms. In the following we show how a meta-notation can also be exploited for the construction of a generic user interface to CORBAs dynamic invocation interface (DII).

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