The propositional logic of ordinary discourse1

Abstract

The logical properties of the ‘if‐then’ connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two‐valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if‐then’. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of ‘if‐then’. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three‐valued logic, its decision procedure is almost as efficient as that of the classical logic. It therefore provides a rational and convenient system in which to formalize English arguments.