A conceptual graph (CG) is a formalism for knowledge representation. In the first published paper on CGs, John F. Sowa used them to represent the conceptual schemas used in database systems. The first book on CGs 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: a graphical interface for first-order logic, a diagrammatic calculus of logics, and a graph-based knowledge representation and reasoning model.

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)))