Distribution in the logic of meaning containment and in quantum mechanics

Ross T. Brady

Andrea Meinander

pp. 223-255

in: Koji Tanaka, Francesco Berto, Edwin D. Mares, Francesco Paoli (eds), Paraconsistency, Berlin, Springer, 2013

Abstract

The paper examines the sentential and quantificational forms of distribution in classical, intuitionistic and relevant logics, and in relation to quantum mechanics. Particular attention is also paid to the first author's logic MCQ of meaning containment. The ultimate aim is to determine whether distribution should be included and, if so, in what forms. We conclude that the sentential and existential rule-forms, both derivable from the two-premise meta-rules of MCQ, are the only two forms that generally hold.