A Semantic Algebra for Cognitive Linguistics and Cognitive Computing

Semantics is the meaning of a l anguage unit at the levels of word, phrase, sentence, paragraph, and essay. Cognitive linguistics foc uses on cognitive sem antics of sentences and its in teraction with syntactic structures. A denotational mathematical framework of language semantics known as se mantic algebra is developed in this paper. Semantic algebra reveals the nature of semantics by a general mathematical model. On the b asis of the form al semantic structure, language semantics can be deductively manipulated by a set of al gebraic operations at different levels oft anguage units. According to semantic algebra, semantic interpretation and comprehension can be embodied as a process of formal semantic aggregation in c ognitive linguistics from the botto m up. Applications of semantic algebra are illustrated in computational linguistics, c omputing with words, cognitive informatics, and cognitive computing.