Editing Conceptual graph (section)

=== Graphical interface for first-order logic ===
[[File:Cat-on-mat.svg|thumb|left|250px|Elsie the cat is sitting on a mat]]
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:

{{code|[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:

{{code|(exists ((x Sitting) (y Mat)) (and (Cat Elsie) (agent x Elsie) (location x y)))}}

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

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