Journal of Philosophical Logic

, Volume 41, Issue 4, pp 671-709

First online:

Consequence Mining

Constants Versus Consequence Relations
  • Denis BonnayAffiliated withDépartement de Philosophie, Université Paris Ouest Nanterre Email author 
  • , Dag WesterståhlAffiliated withUniversity of GothenburgStockholm University

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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 \(\Rightarrow_X\). 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.


Consequence relation Constant Logical constant Bolzano Tarski Galois connection Replacement Substitution