Logic of Determination of Objects: The Meaning of Variable in Quantification

Jean-Pierre Descles, Université de Paris-Sorbonne; and Anca Pascu, Université de Bretagne Occidentale

This article constitutes a contribution to an analysis of the notion of variable. Whithin the framework of Combinatory Logic as a formalism without bound variables, the Logic of Determination of Objects (LDO) provides an explanation for the necessary distinction between whatever, any, and indeterminate, indefinite used by the introduction and elimination rules of quantifiers in Natural Deduction. The intension of a concept and typical and atypical occurences of a concept are also introduces yielding new quantifiers which are more adequate to natural language processing (NLP) and to the study of natural inferences in common reasoning.


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