Conceptual graphs

Conceptual graphs (CGs) are a formalism for knowledge representation. In the first published paper on CGs, John F. Sowa (Sowa 1976) used them to represent the conceptual schemas used in database systems. The first book on CGs (Sowa 1984) applied them to a wide range of topics in artificial intelligence, computer science, and cognitive science.

Since 1984, the model has been developed along three main directions.

In this approach, a formula in first-order logic (predicate calculus) is represented by a labeled graph.

A linear notation, called the Conceptual Graph Interchange Format (CGIF), has been standardized in the ISO standard for common logic.

The diagram above is an example of the display form for a conceptual graph. Each box is called a concept node, and each oval is called a relation node. In CGIF, this CG would be represented by the following statement: [Cat Elsie] [Sitting *x] [Mat *y] (agent ?x Elsie) (location ?x ?y)

In CGIF, brackets enclose the information inside the concept nodes, and parentheses enclose the information inside the relation nodes. The letters x and y, which are called coreference labels, show how the concept and relation nodes are connected. In CLIF, those letters are mapped to variables, as in the following statement: (exists ((x Sitting) (y Mat)) (and (Cat Elsie) (agent x Elsie) (location x y)))

As this example shows, the asterisks on the coreference labels *x and *y in CGIF map to existentially quantified variables in CLIF, and the question marks on ?x and ?y map to bound variables in CLIF. A universal quantifier, represented @every*z in CGIF, would be represented forall (z) in CLIF.

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