Classical and Intuitionistic Subexponential Logics are Equally Expressive

Kaustuv Chaudhuri

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arXiv · 1006.3134

Classical and Intuitionistic Subexponential Logics are Equally Expressive

Kaustuv Chaudhuri

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Abstract

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.

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BibTeX RIS

Kaustuv Chaudhuri. 2010-06-16. Classical and Intuitionistic Subexponential Logics are Equally Expressive. https://arxiv.org/abs/1006.3134

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