Conceptual graphs for by Jean Fargues Marie - Claude Landau

ion operator was introduced as the lambda abstraction operator because this semantic model is based on a particular interpretation of the typed lambda calculus used to denote natural language semantics. Thus, a particular “pen” can be denoted by the 0-order expression h()[pen 1231, the class of all pens can be defined by the 1-order expression h(x)[pen(x)], and this class is a particular subclass of the class noted by the second-order expression h(P)[writingartifacts(P)], where the functional variable P can be instantiated to the class “pen.” play an instrument y by a logical form such as In the Montague semantics-based approach [3], the It is also possible to define the class of all musicians who set of all conceptual graphs. X(x,y)[person(x) A play(x,y) A music-instrument(y)] or by the functional expression X(x,y)[play(person(x),music-instrument(y))]. The conceptual graph model also allows us to define new concepts and new conceptual relations using an abstraction operation. We give in Figure 4 an example of definition statements for a new concept and for a new conceptual relation. Whenever a definition is given, the new concept is added to the concept type lattice: In the example following, ARTSPONSOR < PERSON will be stored in the lattice. The contraction operation takes as arguments a conceptual graph and a definition. It tries to replace a subgraph of the given conceptual graph by a single concept (or relation) using the definition of this concept. This contraction process also takes into account the restriction relation on the concepts of the conceptual graph in which the substitution is applied (see Figure 5). The contraction algorithm applies a partial substitution when the graph to be contracted is more restricted, as shown in Figure 6 . Thus, we do not lose the information which was contained in the original graph. It is sometimes possible to perform several contractions on the same graph when this graph contains multiple occurrences of the definition graph. In this case, the contraction algorithm may be iterated on the graph obtained at each step. Another useful algorithm is the expansion algorithm, which unfolds a single concept (or relation) occumng in a conceptual graph by replacing this occurrence with its definition graph. From syntax to semantics using conceptual graphs A classical property of the formal models for natural language semantics used in AI is that they obey the compositionality principle. It is usually assumed that a representation of the semantics of an entire sentence can be built by combining the semantic representations associated with its components. syntactic tree to build the semantic representation of the sentence. A semantic form is assumed to be given (or selected) for each word in a semantic lexicon. An operator is defined to build the semantic form attached to a parent node of the syntactic tree. This operator takes as arguments the semantic forms attached to the son's nodes and gives as result a more complex composed semantic form. If we consider the Montague semantic approach or related work such as [ 1 I ] , logical forms describing the semantics of the words in the lexicon can be represented as expressions in the lambda-calculus formalism. The operator which combines the logical forms to obtain a semantic representation for a sentence is in this case the lambdaevaluation operator (see Figure 7). The lambda expression of A classical approach consists of starting from a traditional