A formulae-as-type notion of control
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A semantics of evidence for classical arithmetic
Journal of Symbolic Logic
Towards Limit Computable Mathematics
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
An Arithmetical Hierarchy of the Law of Excluded Middle and Related Principles
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Can Proofs be Animated by Games?
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
Semantics for intuitionistic arithmetic based on Tarski games with retractable moves
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Non-commutative first-order sequent calculus
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Hi-index | 0.00 |
This paper shows the equivalence for provability between two infinitary systems with the ω-rule. One system is the positive one-sided fragment of Peano arithmetic without Exchange rules. The other system is two-sided Heyting Arithmetic plus the law of Excluded Middle for Σ10 -formulas, and it includes Exchange. Thus, the logic underlying positive Arithmetic without Exchange, a substructural logic, is shown to be a logic intermediate between Intuitionism and Classical Logic, hence a subclassical logic. As a corollary, the authors derive the equivalence for positive formulas among provability in those two systems and validity in two apparently unrelated semantics: Limit Computable Mathematics, and Game Semantics with 1-backtracking.