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Neuro-cognitive and psychological linguistics present important area of multidisciplinary research.
In this paper we have described some possible applications of mathematical methods to neuro-cognitive linguistics. In neuro-cognitive study of language, neural architecture and neuropsychological mechanism of verbal cognition are basis of a vector–based modeling. A comparison of human mental space to a vector space is an effective way of analyzing of human semantic vocabulary, mental representations and rules of clustering and mapping in typologically different languages.
Euclidean and non-Euclidean spaces can be applied for a description of human semantic vocabulary and high order structures reflecting internal and external features of object and action (event). Vector analysis of word meaning and basic syntax structures offers new methodological opportunities to interpret effect of semantic and pragmatic forces at morphology and syntax levels.
Non-linear and metaphoric transformations present specific complex phenomenon to be described in 3D and other N-dimensional spaces in the framework of quantum semantics.
Keywords: Mental mapping, human mental lexicon, embodied and symbolic cognition, verbal cognition, semantic space, scalar, vector space, mental transformation, semantic gravity.