A formal grammar is a set of symbols and the production rules for rewriting some of them into every possible string of a formal language over an alphabet. A grammar does not describe the meaning of the strings –only their form.
In applied mathematics, formal language theory is the discipline that studies formal grammars and languages. Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas.
In linguistics, the syntax–semantics interface is the interaction between syntax and semantics. Its study encompasses phenomena that pertain to both syntax and semantics, with the goal of explaining correlations between form and meaning. Specific topics include scope, binding, and lexical semantic properties such as verbal aspect and nominal individuation, semantic macroroles, and unaccusativity.
The interface is conceived of very differently in formalist and functionalist approaches. While functionalists tend to look into semantics and pragmatics for explanations of syntactic phenomena, formalists try to limit such explanations within syntax itself. Aside from syntax, other aspects of grammar have been studied in terms of how they interact with semantics; which can be observed by the existence of terms such as morphosyntax–semantics interface.
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