Abstract
Semantics is the meaning of a language unit at the levels of word, phrase, sentence, paragraph, and essay. Cognitive linguistics focuses on cognitive semantics of sentences and its interaction with syntactic structures. A denotational mathematical framework of language semantics known as semantic algebra is developed in this paper. Semantic algebra reveals the nature of semantics by a general mathematical model. On the basis of the formal semantic structure, language semantics can be deductively manipulated by a set of algebraic operations at different levels of language units. According to semantic algebra, semantic interpretation and comprehension can be embodied as a process of formal semantic aggregation in cognitive linguistics from the bottom up. Applications of semantic algebra are illustrated in computational linguistics, computing with words, cognitive informatics, and cognitive computing.
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