Classical and Intuitionistic Subexponential Logics are Equally Expressive [article]

Kaustuv Chaudhuri
2010 arXiv   pre-print
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
more » ... his 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.
arXiv:1006.3134v1 fatcat:mlzrr7v4ajb7nm5h2nfpbhnswi