An order-theoretic analysis of interpretations among propositional deductive systems

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Abstract

In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have different underlying languages.

MSC

03G27
06F07

Keywords

Consequence relation
Translation
Interpretation
Quantale

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