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A. J. Baker (1955). Incompatible Hypotheticals and the Barber Shop Paradox.

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    The Propositional Logic of Ordinary Discourse.William S. Cooper - 1968 - Inquiry 11 (1-4):295 – 320.
    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 (...)
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