Inductive inference hierarchies: probabilistic vs pluralistic strategies
Proceedings of the International Spring School on Mathematical method of specification and synthesis of software systems '85
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Probability and plurality for aggregations of learning machines
Information and Computation
Probabilistic inductive inference
Journal of the ACM (JACM)
Can finite samples detect singularities of real-valued functions?
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Probabilistic language learning under monotonicity constraints
Theoretical Computer Science - Special issue on algorithmic learning theory
On the relative sizes of learnable sets
Theoretical Computer Science
The Power of Pluralism for Automatic Program Synthesis
Journal of the ACM (JACM)
Probabilistic inductive inference: a survey
Theoretical Computer Science
Classification using information
Annals of Mathematics and Artificial Intelligence
Logic Programming with Bounded Quantifiers
Proceedings of the First Russian Conference on Logic Programming
Learning Formulae from Elementary Facts
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
Learning, Logic, and Topology in a Common Framework
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
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Suppose we are given a set W of logical structures, or possible worlds, a set of logical formulas called possible data and a logical formula @f. We then consider the classification problem of determining in the limit and almost always correctly whether a possible world M satisfies @f, from a complete enumeration of the possible data that are true in M. One interpretation of almost always correctly is that the classification might be wrong on a set of possible worlds of measure 0, with respect to some natural probability distribution over the set of possible worlds. Another interpretation is that the classifier is only required to classify a set W^' of possible worlds of measure 1, without having to produce any claim in the limit on the truth of @f for the members of the complement of W^' in W. We compare these notions with absolute classification of W with respect to a formula that is almost always equivalent to @f in W, hence we investigate whether the set of possible worlds on which the classification is correct is definable. We mainly work with the probability distribution that corresponds to the standard measure on the Cantor space, but we also consider an alternative probability distribution proposed by Solomonoff and contrast it with the former. Finally, in the spirit of the kind of computations considered in Logic programming, we address the issue of computing almost correctly in the limit witnesses to leading existentially quantified variables in existential formulas.