PX: a computational logic
Type systems for programming languages
Handbook of theoretical computer science (vol. B)
Towards the animation of proofs---testing proofs by examples
Theoretical Computer Science - Special issue on theories of types and proofs
Learning in Logic with RichProlog
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
Towards Limit Computable Mathematics
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Learning Algebraic Structures from Text Using Semantical Knowledge
ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
Mathematics based on incremental learning: excluded middle and inductive inference
Theoretical Computer Science - Algorithmic learning theory(ALT 2002)
Learning Bounded Unions of Noetherian Closed Set Systems Via Characteristic Sets
ICGI '08 Proceedings of the 9th international colloquium on Grammatical Inference: Algorithms and Applications
Prediction of recursive real-valued functions from finite examples
JSAI'05 Proceedings of the 2005 international conference on New Frontiers in Artificial Intelligence
Inductive logic programming: yet another application of logic
INAP'05 Proceedings of the 16th international conference on Applications of Declarative Programming and Knowledge Management
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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 the subjects of studies are mathematical objects, the objective of the studies are learning. In this paper, a mathematics of which 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.