Abstract
It is recognized that formal grammars and rigorous syntactic rules are indispensable in formal, cognitive, and computational linguistics. The formal syntax of linguistics can be classified into two categories known as the analytic and synthetic syntax. The former are a set of lexical rules of individual words, phrases, and parts of speech; while the latter are a set of relational rules of formal syntaxes within and beyond sentences. The synthetic syntaxes can be formally embodied by a set of relational syntactic rules for lexis, phrases, and parts of speech within and beyond sentences. A theoretical framework of formal linguistics is coherently presented by analytic and synthetic syntaxes based on contemporary denotational mathematics. The formalization of natural language syntaxes and grammars enables a wide range of applications not only in cognitive informatics, cognitive linguistics, natural language processing, cognitive computing, semantic computing, cognitive robotics, and computational linguistics in general, but also in word processing, web search engines, online text processing, machine-enabled language comprehension, autonomous machine learning, cognitive translators, computing with words, and cognitive systems in particular.
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