Conceptual Graph - A Graphical Interface For First-order Logic

A Graphical Interface For First-order Logic

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 on the right 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:

(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 the Common Logic Interchange Format (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.

Reasoning can be done by translating graphs into logical formulas, then applying a logical inference engine.