Trivalent Logics and Their Applications

Trivalent logics have been an object of extensive study since at least the work of Lukasiewicz, with applications to a wide range of natural language phenomena, including presupposition, conditionals and vagueness. While many-valued logics can be studied on their own, there has been a regain of interest for three-valued logics in recent years, with the emergence of new perspectives regarding their applicability to natural language.

In the theory of presupposition projection, in particular, the question of whether the projection of presupposition can be dealt with by means of a trivalent truth-functional semantics has been the object of renewed attention, in particular because truth-functional trivalent approaches appear as a main competitor to both dynamic and pragmatic approaches (viz. Beaver and Krahmer 2001, George 2008, Fox 2008, all of them giving special attention to so-called middle-Kleene logic proposed by Peters, and the recent debates with Schlenker). In the area of vagueness, ways have been proposed to combine the canonical paracomplete and paraconsistent three-valued logics of Kleene and Priest in order to deal with the paradoxes of vagueness, and to account for phenomena such as meaning coarsening and strengthening (viz. Avron et Konikowska 2008, Cobreros et al. 2010). In the literature on conditionals, finally, the question remains largely open of the selection between a wide range of candidates for the definition of a suitable three-valued conditional (viz. Bradley 2002, Cantwell 2008, Huitink 2009, Rothschild 2009). From a more foundational point of view, finally, the meaning attached to the third truth value can vary significantly depending on the problem under consideration and the definition of logical consequence considered to be relevant.

The aim of this workshop is to solicit new contributions for the extension of two-valued logic with a third truth-value.