We present a new logical formalism, called Logic of Determination of Objects (LDO). This logic gives a formal approach to the following cognitive elements which do not studied by classical logic: notion of object, operation of determination and notions of typicality and atypicality. These notions are expressed by natural languages, but they are not taken into account by the first order calculus. As for quantification, there is a break between Frege’s quantification and the quantification operations expressed by natural language semiotic organizations. LDO formalizes different objects (more or less determinate objects), the operators of determination acting on objects and the typical object canonically associated to a concept, with a theory of typicality (in Rosch’s sense) and a quantification theory larger than the ones from classical logic and from linguistics. LDO seems to be a tool better adapted to natural language analysis, to natural language processing (NLP) systems and to ontologies building.
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