PX: a computational logic
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
Test Driven Development: By Example
Test Driven Development: By Example
Towards Limit Computable Mathematics
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
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
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
Toward the interpretation of non-constructive reasoning as non-monotonic learning
Information and Computation
Interactive Learning-Based Realizability Interpretation for Heyting Arithmetic with EM1
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Computing characteristic sets of bounded unions of polynomial ideals
JSAI'07 Proceedings of the 2007 conference on New frontiers in artificial intelligence
A new translation for semi-classical theories: backtracking without CPS
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Can proofs be animated by games?
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Interactive Realizers: A New Approach to Program Extraction from Nonconstructive Proofs
ACM Transactions on Computational Logic (TOCL)
Can Proofs be Animated by Games?
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
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Learning theoretic aspects of mathematics and logic have been studied by many authors. They study how mathematical and logical objects are algorithmically "learned" (inferred) from finite data. Although they study mathematical objects, the objective of the studies is learning. In this paper, a mathematics whose foundation itself is learning theoretic will be introduced. It is called Limit-Computable Mathematics. It was originally introduced as a means for "Proof Animation", which is expected to make interactive formal proof development easier. Although the original objective was not learning theoretic at all, learning theory is indispensable for our research. It suggests that logic and learning theory are related in a still unknown but deep new way.