Classical and Intuitionistic Subexponential Logics Are Equally Expressive [chapter]

Kaustuv Chaudhuri
2010 Lecture Notes in Computer Science  
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. Γ ⊢ [P] ; Q − Γ ; [N] ⊢ · Γ ; [P ⊸ N] ⊢ Q −
doi:10.1007/978-3-642-15205-4_17 fatcat:2wu4xiliovdatgokl2mb6abzva