  Grammar formalisms—special-purpose systems for the description of linguistic systems and subsystems—can be thought of as logics designed to axiomatize the association of linguistic structures with strings of symbols. You might be able to infer from such a system, for instance, that ‘assignments’ is the plural form of the nominalization of the verb ‘assign’. So you can look at the process of parsing a string of words—of finding the linguistic structures, if any, that are associated with it—as a search for a proof in a certain logical system.