Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Saving the phenomena: requirements that inductive inference machines not contradict known data
Information and Computation
On uniform learnability of language families
Information Processing Letters
On the role of procrastination in machine learning
Information and Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
A Guided Tour Across the Boundaries of Learning Recursive Languages
Algorithmic Learning for Knowledge-Based Systems, GOSLER Final Report
Robust Learning with Infinite Additional Information
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
Learning with Higher Order Additional Information
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
On Approximately Identifying Concept Classes in the Limit
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
Identifiability of Subspaces and Homomorphic Images of Zero-Reversible Languages
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
The Complexity of Universal Text-Learners
FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
Synthesizing inductive expertise
Information and Computation
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
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The present work investigates to which extent semantical knowledge can support the learning of basic mathematical concepts. The considered learning criteria are learning characteristic or enumerable indices for languages from positive data where the learner has to converge either syntactically (Ex) or semantically (BC). The considered classes are the classes of all monoids of a given group, all ideals of a given ring or all subspaces of a given vector space. The following is shown: (a) Learnability depends much on the amount of semantic knowledge given at the synthesis of the learner where this knowledge is represented by programs for the algebraic operations, codes for prominent elements of the algebraic structure (like 0 and 1 in fields) and certain parameters (like the dimension of finite dimensional vector spaces). For several natural examples good knowledge of the semantics may enable to keep ordinal mind change bounds while restricted knowledge may either allow only BC-convergence or even not permit learnability at all. (b) A recursive commutative ring is Noetherian iff the class of its ideals is BC-learnable. Such a BC-learner can be synthesized from programs for addition and multiplication. In many Noetherian rings, one can Ex-learn characteristic indices for the ideals with an ordinal bound on the number of mind changes. But there are also some Noetherian rings where it is impossible to Ex-learn the ideals or to learn characteristic indices for them.