An Investigation of Logical Pluralism and B-entailment
Logical pluralism. Multivalued logic. B-entailment. Consequence relation.
In the present thesis the framework of B-entailment in [Blasio and Marcos, ], unpublished, is examined in terms of some main theories of logical pluralism. Starting with the form of pluralism postulated by Shapiro [Shapiro, 2014], which takes an eclectic approach to logic and discusses pluralism at several levels. This thesis examines also the form of pluralism defended by Beall and Restall [Beall and Restall, 2006], Restall [Restall, 2014], and Hjortland [Hjortland, 2013]. Beall and Restall propose a form of pluralism based on the vagueness of the notion of logical consequence, while Restall explores a form of pluralism through proof-theory. Hjortland criticises both of these approaches presenting his own, based somewhat on Restall’s. This thesis then presents B-entailment as a four-place consequence relation that can simulate other consequence relations. It has a non-deterministic and cognitive attitude semantics, which lends it a broad expressive power. A method of providing a sequent calculus for the logics simulated by B-entailment is provided, and this frameworkis examined in the light of the forms of pluralisms presented.