Classical and Intuitionistic Subexponential Logics Are Equally Expressive
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.
Unable to display preview. Download preview PDF.
- 2.Barber, A., Plotkin, G.: Dual intuitionistic linear logic. Technical Report ECS-LFCS-96-347, University of Edinburgh (1996)Google Scholar
- 3.Chang, B.-Y.E., Chaudhuri, K., Pfenning, F.: A judgmental analysis of linear logic. Technical Report CMU-CS-03-131R, Carnegie Mellon University (December 2003)Google Scholar
- 4.Chaudhuri, K.: The Focused Inverse Method for Linear Logic. PhD thesis, Carnegie Mellon University, Technical report CMU-CS-06-162 (December 2006)Google Scholar
- 6.Chaudhuri, K.: Classical and intuitionistic subexponential logics are equally expressive. Technical report, INRIA (2010)Google Scholar
- 10.Laurent, O.: Etude de la polarisation en logique. Thèse de doctorat, Université Aix-Marseille II (March 2002)Google Scholar
- 12.Liang, C., Miller, D.: A unified sequent calculus for focused proofs. In: LICS-24, pp. 355–364 (2009)Google Scholar
- 13.Miller, D.: Finding unity in computational logic. In: ACM-BCS-Visions (April 2010)Google Scholar
- 14.Nigam, V.: Exploiting non-canonicity in the sequent calculus. PhD thesis, Ecole Polytechnique (September 2009)Google Scholar
- 15.Nigam, V., Miller, D.: Algorithmic specifications in linear logic with subexponentials. In: PPDP, pp. 129–140 (2009)Google Scholar