Classical and Intuitionistic Subexponential Logics Are Equally Expressive

  • Kaustuv Chaudhuri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6247)


It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the other direction has no truth-preserving propositional encodings. We show here that subexponential logic, which is a family of substructural refinements of classical logic, each parametric over a preorder over the subexponential connectives, does not suffer from this asymmetry if the preorder is systematically modified as part of the encoding. Precisely, we show a bijection between synthetic (i.e., focused) partial sequent derivations modulo a given encoding. Particular instances of our encoding for particular subexponential preorders give rise to both known and novel adequacy theorems for substructural logics.


Inference Rule Classical Logic Intuitionistic Logic Linear Logic Sequent Calculus 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Kaustuv Chaudhuri
    • 1
  1. 1.INRIA SaclayFrance

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