PX: a computational logic
Theory of algebraic invariants
Theory of algebraic invariants
Complexity and real computation
Complexity and real computation
Towards the animation of proofs---testing proofs by examples
Theoretical Computer Science - Special issue on theories of types and proofs
Limiting Partial Combinatory Algebras towards Infinitary Lambda-Calculi and Classical Logic
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Algebraically generalized recursive function theory
IBM Journal of Research and Development
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
Limiting Partial Combinatory Algebras towards Infinitary Lambda-Calculi and Classical Logic
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
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
Learnable algorithm on the continuum
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Positive arithmetic without exchange is a subclassical logic
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
A new translation for semi-classical theories: backtracking without CPS
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Prefix-Like complexities and computability in the limit
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Can proofs be animated by games?
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Can Proofs be Animated by Games?
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
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The notion of Limit-Computable Mathematics (LCM) will be introduced. LCM is a fragment of classical mathematics in which the law of excluded middle is restricted to 驴20-formulas. We can give an accountable computational interpretation to the proofs of LCM. The computational content of LCM-proofs is given by Gold's limiting recursive functions, which is the fundamentalno tion of learning theory. LCM is expected to be a right means for "Proof Animation", which was introduced by the first author [10]. LCM is related not only to learning theory and recursion theory, but also to many areas in mathematics and computer science such as computational algebra, computability theories in analysis, reverse mathematics, and many others.