From constants to consequence, and back

Synthese 187 (3):957-971 (2012)
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Abstract

Bolzano’s definition of consequence in effect associates with each set X of symbols (in a given interpreted language) a consequence relation X . We present this in a precise and abstract form, in particular studying minimal sets of symbols generating X . Then we present a method for going in the other direction: extracting from an arbitrary consequence relation its associated set C of constants. We show that this returns the expected logical constants from familiar consequence relations, and that, restricting attention to sets of symbols satisfying a strong minimality condition, there is an isomorphism between the set of strongly minimal sets of symbols and the set of corresponding consequence relations (both ordered under inclusion).

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Dag Westerståhl
Stockholm University

Citations of this work

Logical Consequence.J. C. Beall, Greg Restall & Gil Sagi - 2019 - Stanford Encyclopedia of Philosophy.
Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
Consequence Mining: Constans Versus Consequence Relations.Denis Bonnay & Dag Westerståhl - 2012 - Journal of Philosophical Logic 41 (4):671-709.

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