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Although it is well known that the full meaning of a concept includes an intensional and an extensional aspect, the latter is neglected in almost all practically used knowledge representations and semantic formalisms, which consider only the interrelationships between concepts but not their referential meaning. In logically oriented representations with the usual model-theoretic interpretation, the extensions of predicates or symbols of the language in general belong to a metalevel (the model level) clearly distinguished from the logical language. In this paper, we show in what way the extensional aspect is important (in addition to the intensional aspect) to account for the full meaning of natural language expressions. The necessity of dealing with both types of meaning is illustrated by means of semantic phenomena like factual and intensional negation, intensional quantification and cardinalities, or by the meaning of prepositions describing set relationships, and others. We will utilize the framework of Multilayered Extended Semantic Networks (MultiNet) to discuss these issues. The MultiNet formalism is successfully used in various NLP applications. Its explicit modeling of intensional and preextensional layers offers an explanation of the interplay of intension and extension of conceptual entities in the overall process of constituting the meaning representations of natural language expressions.

The Role of Intensional and Extensional Interpretation in Semantic Representations – The Intensional and Preextensional Layers in MultiNet