Consequence Mining: Constans Versus Consequence Relations

Journal of Philosophical Logic 41 (4):671-709 (2012)
The standard semantic definition of consequence with respect to a selected set X of symbols, in terms of truth preservation under replacement (Bolzano) or reinterpretation (Tarski) of symbols outside X, yields a function mapping X to a consequence relation ⇒x. We investigate a function going in the other direction, thus extracting the constants of a given consequence relation, and we show that this function (a) retrieves the usual logical constants from the usual logical consequence relations, and (b) is an inverse to—more precisely, forms a Galois connection with—the Bolzano-Tarski function
Keywords Consequence relation  Constant  Logical constant  Bolzano  Tarski  Galois connection  Replacement  Substitution
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DOI 10.1007/s10992-012-9234-6
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References found in this work BETA
Rudolf Carnap (1937). The Logical Syntax of Language. London, K. Paul, Trench, Trubner & Co., Ltd..
John Corcoran & Alfred Tarski (1986). What Are Logical Notions? History and Philosophy of Logic 7 (2):143-154.

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