Béziau on and and or

Lloyd Humberstone

pp. 283-307

in: Arnold Koslow, Arthur Buchsbaum (eds), The road to universal logic I, Basel, Birkhäuser, 2015

Abstract

We offer a commentary on aspects of Béziau's work on combining the logic of conjunction with that of disjunction, concentrating on the most recent incarnation of this work in a paper ("To Distribute or Not to Distribute?") co-authored with M. Coniglio. After some opening remarks we consider the issues of distribution and absorption (Sects. 2 and 3), a discussion naturally leading to the question of whether in the weaker of two senses of "combined logic"—roughly, combined consequence relation rather than combined proof system based on the standard rules—the combined logic of conjunction and disjunction has a finite (strictly) characteristic matrix (Sect. 4). Section 5 takes a brief look at this consequence relation from the perspective of bivalent valuational semantics.

Cited authors

Béziau Jean-Yves