Abstract
Semantics is composed meaning of language expressions and perceptions at the levels of words, phrase, sentence, paragraph, and essay. The basic unit of formal semantics is a concept as a formal model of words in a natural language. Cognitive linguistics focuses on cognitive semantics and its interaction with underlying syntactic structures. A denotational mathematics known as semantic algebra is presented for rigorous semantics manipulations in cognitive linguistics. Semantic algebra deals with formal semantics of linguistics by a general mathematical model of semantics and a set of algebraic operators. On the basis of semantic algebra, language semantics may not only be deductively analyzed based on syntactic structures from the top down, but also be synthetically composed by the algebraic semantic operators from the bottom up at different levels of language units. Semantic algebra enables a wide range of applications in cognitive informatics, cognitive linguistics, computational linguistics, semantic computing, cognitive computing, machine learning, computing with words, as well as natural language analysis, synthesis, and comprehension.
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