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Concept
Conceptual graph
Summary
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:
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:
As this example shows, the asterisks on the coreference labels and in CGIF map to existentially quantified variables in CLIF, and the question marks on and map to bound variables in CLIF. A universal quantifier, represented in CGIF, would be represented in CLIF.
Reasoning can be done by translating graphs into logical formulas, then applying a logical inference engine.
Another research branch continues the work on existential graphs of Charles Sanders Peirce, which were one of the origins of conceptual graphs as proposed by Sowa. In this approach, developed in particular by Dau , conceptual graphs are conceptual diagrams rather than graphs in the sense of graph theory, and reasoning operations are performed by operations on these diagrams.
Official source
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