Inquiry 11 (1-4):295 – 320 (1968)
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.
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References found in this work BETA
The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1931 - Paterson, N.J., Littlefield, Adams.
Aristotle's Syllogistic From the Standpoint of Modern Formal Logic.Jan Łukasiewicz - 1951 - Garland.
Citations of this work BETA
New Foundations for Imperative Logic I: Logical Connectives, Consistency, and Quantifiers.Peter B. M. Vranas - 2008 - Noûs 42 (4):529-572.
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Relevant Restricted Quantification.J. C. Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall - 2006 - Journal of Philosophical Logic 35 (6):587-598.
The Revival of Rejective Negation.Lloyd Humberstone - 2000 - Journal of Philosophical Logic 29 (4):331-381.
Everyday Reasoning and Logical Inference.Jon Barwise - 1993 - Behavioral and Brain Sciences 16 (2):337.
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