In this approach, a formula in first-order logic is represented by a labeled graph. A linear notation, called the Conceptual Graph Interchange Format, 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.
Diagrammatic calculus of logics
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.
Graph-based knowledge representation and reasoning model
Key features of GBKR, the graph-based knowledge representation and reasoning model developed by Chein and Mugnier and the Montpellier group, can be summarized as follows:
All kinds of knowledge are labeled graphs, which provide an intuitive and easily understandable means to represent knowledge.
Reasoning mechanisms are based on graph notions, basically the classical notion of graph homomorphism; this allows, in particular, to link basic reasoning problems to other fundamental problems in computer science.
Sentence generalization and generalization diagrams can be defined as a special sort of conceptual graphs which can be constructed automatically from syntactic parse trees and support semantic classification task. Similarity measure between syntactic parse trees can be done as a generalization operation on the lists of sub-trees of these trees. The diagrams are representation of mapping between the syntax generalization level and semantics generalization level. Generalization diagrams are intended to be more accurate semantic representation than conventional conceptual graphs for individual sentences because only syntactic commonalities are represented at semantic level.
