Consequence Mining: Constans Versus Consequence Relations

Journal of Philosophical Logic 41 (4):671-709 (2012)
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Abstract

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

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2012-05-26

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Author Profiles

Denis Bonnay
Université Paris Nanterre
Dag Westerståhl
Stockholm University

Citations of this work

Logical Consequence.J. C. Beall, Greg Restall & Gil Sagi - 2019 - Stanford Encyclopedia of Philosophy.
Logical Form: Between Logic and Natural Language.Andrea Iacona - 2018 - Cham, Switzerland: Springer Verlag.
Toward a general theory of knowledge.Luis M. Augusto - 2020 - Journal of Knowledge Structures and Systems 1 (1):63-97.

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References found in this work

Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
The Logical Syntax of Language.Rudolf Carnap - 1937 - London: K. Paul, Trench, Trubner & Co..
What are logical notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
The Ways of Paradox.W. V. O. Quine - 1966 - New York: Random.
Quantifiers in Language and Logic.Stanley Peters & Dag Westerståhl - 2006 - Oxford, England: Clarendon Press.

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