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3.5.3.2. Conceptual Approaches: The Conceptual Graphs

"Conceptual Graphs" (CGs) is a knowledge representation system that makes use of a graph based notation and is specially devoted to the representation of NL semantics. This particular type of notation has been developed by John Sowa [see Sowa (1991)], originally for incrementing the expressive power of the database languages, and made known to the general public in 1984.

The basic representational primitives used in CGs are (1) the classes of concepts ("concept-types," organized into a type-hierarchy), (2) the "concepts" and the corresponding "referents," and (3) the "conceptual relations." Concept-types represent general classes of entities, attributes, states and events; in NL terms, they correspond not only to nouns, but also to other categories of "lexical words" like verbs, qualitative adjectives, and adverbs. We can, therefore, meet CGs concept-types like CAT, SIT, DANCE, GRACEFUL (corresponding to both the adjective and the adverb "gracefully"), TIME, PERSON, SITUATION, PROPOSITION, etc.; it is assumed that, for any conceptual graphs system, there exists a predefined set of such types, which is different according to the domain to formalize. As already stated, concept-types are inserted into a type-hierarchy; this is, in fact, a lattice defined by a partial ordering relation, "<," which means that some concepts are totally subsumed in others. Therefore, if ANIMAL,CAT, MAMMAL and PHYSICAL-OBJECT are concept-types, they are linked, within the type-hierarchy, by the relationship: CAT < MAMMAL < ANIMAL < PHYSICAL-OBJECT, i.e., MAMMAL is, at the same time, a "super-type" of CAT and a "subtype" of ANIMAL. Like the set inclusion, the relation "<" is transitive and antisymmetric. The type-hierarchy has the appearance of a lattice given that, e.g., a concept like ELEPHANT may be, at the same type, a subtype of both MAMMAL and WILD-ANIMAL. In technical terms, a lattice of types is characterized by the fact that every two types must have at most one maximal common subtype and one minimal common supertype; this condition is not always easy to respect without being obliged to introduce artificial types in the lattice, in the style of a possible WILD-MAMMAL.

A "concept" is an incarnation of a concept-type: a concept like [CAT] represents an (unnamed) entity of type CAT (with the meaning "there exists a cat"), and can be considered as the simplest form of a conceptual graph. Adding a "referent field" to a concept allows one to designate specific individuals. If we know that, e.g., the current cat is named "Yojo," this situation is represented as: [CAT: Yojo], with the meaning "the entity Yojo is a cat." Therefore, a concept "box" is normally divided into two parts: the "type field" on the left side of the colon, and the "referent field" on the right side. In general, an "indexical referent" -- i.e., a definite reference to an entity that is known contextually, but that is not precisely named, as when we make use of the definite article "the" -- is represented making use of the symbol "#" in the referent field. In this way, "the cat" is represented as [CAT: #]. When the referent is identified with one of the entities already known in the system, the serial number of this entity is appended to the # symbol: therefore, [CAT: #123] means that "the entity #123 is a cat." This particular way of indicating the relationship between a concept-type and a referent can be further specialized. For example, plural situations require the use of a new symbol, "*," to indicate a plural referent. The expression "three cats" is then represented as [CAT: {*}@3]. The plural referent {*} indicates here some unspecified entities of the type CAT, and the "qualifier" @3 indicates that there are 3 of them. The same type of solution is adopted in the presence of "quantifiers," as "many" or "all"; the symbolism [CAT: {*}@many] corresponds then to "many cats"; etc.


FIGURE 13A A simple example of conceptual graph.

Finally, "conceptual relations" indicate the roles that the concepts play with respect to each other. They are similar to the "cases" used in the different AI interpretations of the case grammar theory and to the Jackendoff's "thematic roles." Some of the most common CGs conceptual relations are, e.g., AGNT in "LADY is an agent of DANCE," ATTR in "PRETTY is an attribute of LADY," MANR in "GRACEFUL is a manner of DANCE," DEST in "CITY is a destination of GO," etc.


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