There are three basic methods presenting type-logical grammar:axiomatic presentation,Gentzen presentation and ND presentation(i.e. natural deduction presentation) . The presentations have the equal ability of deduction,but each has its own function. Axiomatic presentation would become a multi-modal logic system by being equipped with frame semantics. It is mainly used to discuss the soundness and completeness based on frame semantics. Gentzen presentation would make it easy to search finitely the proofs of theorems and it is specifically designed to solve the problem of decidability. ND presentation reflects the view that grammar is equal to logic and it would make type-calculus intuitive. In the end,we commented another presentation,i.e. ND presentation of labeled tree format.
