Conceptual graph

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Elsie the cat is sitting on a mat
Elsie the cat is sitting on a mat

A conceptual graph (CG) is a notation for logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. 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 (Sowa 1984) applied them to a wide range of topics in artificial intelligence, computer science, and cognitive science. A linear notation, called the Conceptual Graph Interchange Format (CGIF), has been standardized in the Final Committee Draft of the proposed 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:

   [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 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.

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  • Sowa, John F. (1984), Conceptual Structures: Information Processing in Mind and Machine, Addison-Wesley, Reading, MA, 1984.
  • Sowa, John F. (1976), "Conceptual Graphs for a Data Base Interface", IBM Journal of Research and Development 20(4), 336–357, July 1976. PDF file.

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[edit] People

There is a lively worldwide conceptual graphs research community, which began with a series of seven annual workshops that met from 1986 to 1992. In 1993, the workshops were upgraded to the International Conferences on Conceptual Structures (ICCS), which have been held annually in Europe, Australia, and North America. Since the mid 1990s, the ICCS community has broadened its scope to include formal concept analysis (FCA) and other tools and languages for representing and reasoning about concepts. Following is a sample of some currently active researchers on conceptual graphs, many of whom combine CGs with FCA and other notations for logic.

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