Journal of Philosophical Logic

, Volume 41, Issue 4, pp 671–709

Consequence Mining

Constants Versus Consequence Relations

Authors

    • Département de PhilosophieUniversité Paris Ouest Nanterre
  • Dag Westerståhl
    • University of Gothenburg
    • Stockholm University
Article

DOI: 10.1007/s10992-012-9234-6

Cite this article as:
Bonnay, D. & Westerståhl, D. J Philos Logic (2012) 41: 671. doi:10.1007/s10992-012-9234-6

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 outsideX, 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.

Keywords

Consequence relationConstantLogical constantBolzanoTarskiGalois connectionReplacementSubstitution
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© Springer Science+Business Media B.V. 2012