Synthese 187 (3):957-971 (2012)
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).
|Keywords||Logical constants Consequence relations Bolzano consequence|
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References found in this work BETA
The Substitution Interpretation of the Quantifiers.J. Michael Dunn & Nuel D. Belnap Jr - 1968 - Noûs 2 (2):177-185.
Situation Theory and its Applications.Peter Aczel & Conference on Situation Theory and Its Applications - 1993
Citations of this work BETA
Consequence Mining: Constans Versus Consequence Relations.Denis Bonnay & Dag Westerståhl - 2012 - Journal of Philosophical Logic 41 (4):671-709.
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