The Method of Hypersequents in the Proof Theory of Propositional Non-classical Logics

Abstract

Abstract Until not too many years ago, all logics except classical logic (and, perhaps, intuitionistic logic too) were considered to be things esoteric. Today this state of affairs seems to have been completely changed. There is a growing interest in many types of nonclassical logics: modal and temporal logics, substructural logics, paraconsistent logics, non-monotonic logics-the list is long. The diversity of systems that have been proposed and studied is so great that a need is felt by many researchers to try to put some order in the present logical jungle. Thus [Cleave, 1991], [Epstein, 1990] and [Wojcicki, 1988] are three recent books in which an attempt is made to develop a general theoretical framework for the study of logics. On the more pragmatic side, several systems have been developed with the goal of providing a computerized logical framework in which many different logical systems can be implemented in a uniform way. An example is the Edinburgh LF [Harper et al., 1993].