This open access book introduces Vector semantics, which links the
formal theory of word vectors to the cognitive theory of
linguistics. The computational linguists and deep learning
researchers who developed word vectors have relied primarily on the
ever-increasing availability of large corpora and of computers with
highly parallel GPU and TPU compute engines, and their focus is
with endowing computers with natural language capabilities for
practical applications such as machine translation or question
answering. Cognitive linguists investigate natural language from
the perspective of human cognition, the relation between language
and thought, and questions about conceptual universals, relying
primarily on in-depth investigation of language in use. In spite of
the fact that these two schools both have 'linguistics' in their
name, so far there has been very limited communication between
them, as their historical origins, data collection methods, and
conceptual apparatuses are quite different. Vector semantics
bridges the gap by presenting a formal theory, cast in terms of
linear polytopes, that generalizes both word vectors and conceptual
structures, by treating each dictionary definition as an equation,
and the entire lexicon as a set of equations mutually constraining
all meanings.
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