Theoretical Computer Science
The Structure of Exponentials: Uncovering the Dynamics of Linear Logic Proofs
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
The focused inverse method for linear logic
The focused inverse method for linear logic
A Logical Characterization of Forward and Backward Chaining in the Inverse Method
Journal of Automated Reasoning
Focusing Strategies in the Sequent Calculus of Synthetic Connectives
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Algorithmic specifications in linear logic with subexponentials
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
A Unified Sequent Calculus for Focused Proofs
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Focusing and polarization in linear, intuitionistic, and classical logics
Theoretical Computer Science
Finding unity in computational logic
Proceedings of the 2010 ACM-BCS Visions of Computer Science Conference
Magically constraining the inverse method using dynamic polarity assignment
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
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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.