Towards a unified setting for non-monotony and paraconsistency

Abstract

The research programme here proposed concerns the philosophy of logic, especially the long-standing debate about logical monism and pluralism. Monists like Quine uphold the idea that the only right logic is classical logic, other deviant calculi - intuitionistic, paraconsis- tent and, in general, non-classical systems [26, 18, 29] - being essentially based on misconceptions of the very role and meaning of logical connectives [21]. On the opposing side, relativists argue against such alleged uniqueness by supporting a pluralism in which divergent non-classical calculi fit in with different semantical contexts in this way receiving their own epistemological justification [1]. From the applicative point of view, logical pluralism is supported by many well-known research fields like artificial intelligence, cognitive science and recent developments in computer science. Nonetheless, such a pluralistic attitude involves many philosophical problems like those related to the notion of logical consequence and the nature of connectives, which still need further explanation [7, 2].We propose to design a unitary framework able to uniformly encompass classical logic as well as a considerable portion of non-classical logics, especially those dealing with non-monotony and paraconsistency, and in this way reassess and possibly provide a definitive answer for some of the philosophical puzzles involved in logical pluralism [7, 1, 12]. Such a uniform framework is expected to be obtained by means of the control sets logical device, a metalogical apparatus introduced and partially discussed in [6, 9]. The intuitive idea is that a control set gathers all the logical contexts which are supposed to block a certain derivation. Carrying out this task, both syntactical and semantical issues are involved, especially in relation to substructural logics [19] and Logics of Formal Inconsistency [8]. (AU)