Classical and Intuitionistic Subexponential Logics are Equally Expressive

Details Classical and Intuitionistic Subexponential Logics are Equally Expressive Classical and Intuitionistic Subexponential Logics are Equally Expressive

2010-06-16

arxiv.org/abs/1006.3134v1

Computer Science

Logic in Computer Science

15 pages, to appear in 19th EACSL Annual Conference on Computer Science Logic (CSL 2010)

Scientific paper

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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