Before display logic is introduced in Chapter 3, in the present chapter several other ideas of generalizing the standard notion of sequent are first briefly reviewed. At the moment, modal proof theory is developing in many directions, see, for example, . In addition to DL various other generalizations of the standard Gentzen format(s) have been suggested and investigated. The list of approaches dealt with below is not intended to be complete in any sense. These formalisms are either partly related, in spirit at least, to DL or otherwise just give an impression of some ways in which Gentzen’s notion of sequent may be generalized. Kanger-style calculi using ‘spotted formulas’ ,  and relational proof systems for modal and non-classical logics , , , for example, are not considered, and Gabbay’s  theory of labelled deductive systems is not dealt with here either. Labelled tableaux calculi and structured consequence relations are considered in Chapters 7 and 8.
KeywordsProof System Sequent System Natural Deduction Proof Theory Structural Rule
Unable to display preview. Download preview PDF.