An Embedding of Existential Graphs into Concept Graphs with Negations

Conceptual graphs are based on the existential graphs of Peirce and the semantic networks of AI (see [So92]). Existential graphs are composed of three syntactical elements: lines of identity, predicate names and cuts (which are used for negation). In [Da00] and [Da01] we introduced the cuts of existential graphs as new syntactical element to concept graphs. The resulting concept graphs with cuts have at least the expressivity of existential graphs. In this article, we present some ideas how existential graphs can be translated to concept graphs with cuts, or, in other words, how existential graphs can be regarded as special concept graphs with cuts. In order to do this, we provide several examples of existential graphs. We discuss the meanings of these examples and how they should be translated to concept graphs with cuts. After the discussion, we attempt to provide a formal definition of existential graphs and a formal definition of their translation to concept graphs with cuts.