Proofs and types
A semantics of evidence for classical arithmetic
Journal of Symbolic Logic
Towards the animation of proofs---testing proofs by examples
Theoretical Computer Science - Special issue on theories of types and proofs
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
Classical logic as limit completion
Mathematical Structures in Computer Science
Mathematics based on incremental learning: excluded middle and inductive inference
Theoretical Computer Science - Algorithmic learning theory(ALT 2002)
Can Proofs be Animated by Games?
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
A Calculus of Realizers for EM1 Arithmetic (Extended Abstract)
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
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We interpret classical proofs as constructive proofs (with constructive rules for *** , ***) over a suitable structure ${\mathcal N}$ for the language of natural numbers and maps of Gödel's system ${\mathcal{T}}$. We introduce a new Realization semantics we call "Interactive learning-based Realizability", for Heyting Arithmetic plus EM 1 (Excluded middle axiom restricted to $\Sigma^0_1$ formulas). Individuals of ${\mathcal N}$ evolve with time, and realizers may "interact" with them, by influencing their evolution. We build our semantics over Avigad's fixed point result [1], but the same semantics may be defined over different constructive interpretations of classical arithmetic (in [7], continuations are used). Our notion of realizability extends Kleene's realizability and differs from it only in the atomic case: we interpret atomic realizers as "learning agents".