Games and full completeness for multiplicative linear logic
Journal of Symbolic Logic
A semantics of evidence for classical arithmetic
Journal of Symbolic Logic
Iterated Limiting Recursion and the Program Minimization Problem
Journal of the ACM (JACM)
On full abstraction for PCF: I, II, and III
Information and Computation
Information and Computation
"Classical" Programming-with-Proofs in lambdaPASym: An Analysis of Non-confluence
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
About a New Method for Computing in Algebraic Number Fields
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Mathematics based on incremental learning: excluded middle and inductive inference
Theoretical Computer Science - Algorithmic learning theory(ALT 2002)
Interactive Realizers: A New Approach to Program Extraction from Nonconstructive Proofs
ACM Transactions on Computational Logic (TOCL)
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We study an abstract representation of the learning process, which we call learning sequence, aiming at a constructive interpretation of classical logical proofs, that we see as learning strategies, coming from Coquand's game theoretic interpretation of classical logic. Inspired by Gold's notion of limiting recursion and by the Limit-Computable Mathematics by Hayashi, we investigate the idea of learning in the limit in the general case, where both guess retraction and resumption are allowed. The main contribution is the characterization of the limits of non-monotonic learning sequences in terms of the extension relation between guesses.