Relative Interpretations and Substitutional Definitions of Logical Truth and Consequence

In Igor Sedlár & Martin Blicha (eds.), The Logica Yearbook 2019. London, Vereinigtes Königreich: pp. 33 - 47 (2020)
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Abstract
This paper proposes substitutional definitions of logical truth and consequence in terms of relative interpretations that are extensionally equivalent to the model-theoretic definitions for any relational first-order language. Our philosophical motivation to consider substitutional definitions is based on the hope to simplify the meta-theory of logical consequence. We discuss to what extent our definitions can contribute to that.
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