Inductive inference hierarchies: probabilistic vs pluralistic strategies
Proceedings of the International Spring School on Mathematical method of specification and synthesis of software systems '85
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
Probabilistic language learning under monotonicity constraints
Theoretical Computer Science - Special issue on algorithmic learning theory
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
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Given a set $\mathcal{W}$of logical structures, or possible worlds, a set $\mathcal{D}$of logical formulas, or possible data, and a logical formula ϕ, we consider the classification problem of determining in the limit and almost always correctly whether a possible world $\mathcal{M}$satisfies ϕ, from a complete enumeration of the possible data that are true in $\mathcal{M}$. One interpretation of almost always correctly is that the classification might be wrong on a set of possible worlds of measure 0, w.r.t. some natural probability distribution over the set of possible worlds. Another interpretation is that the classifier is only required to classify a set $\mathcal{W}'$of possible worlds of measure 1, without having to produce any claim in the limit on the truth of ϕ in the members of the complement of $\mathcal{W}'$in $\mathcal{W}$. We compare these notions with absolute classification of $\mathcal{W}$w.r.t. a formula that is almost always equivalent to ϕ in $\mathcal{W}$, hence investigate whether the set of possible worlds on which the classification is correct is definable. 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.