Abstract: Systemic-Functional Grammar is a theory of grammar and grammatics, based on “grammatical logic”. This paper, starting from the origins of and relations between grammar and logic, discusses essential characteristics of grammatical logic and the issues it deals with, and points out that grammatical logic evolves from natural logic, parallels mathematical logic, but is more inclusive and more explanatory than mathematical logic. In modeling natural language, grammatical logic has touched upon some fundamental problems in many fields of modern logic.