Tracking probabilistic truths: a logic for statistical learning

Abstract We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty represent the agent’s probability, we consider plausibility map, associating to each possible distribution ranking. Beliefs are defined as in Belief Revision Theory, terms of truth most plausible worlds (or more generally, all that enough). two forms conditioning or belief update, corresponding acquisition types information: (1) learning observable evidence obtained by repeated sampling from distribution; (2) higher-order information distribution. The first changes only map (via ‘plausibilistic’ version Bayes’ Rule), but leaves given set distributions essentially unchanged; second rules out some distributions, thus shrinking possibilities, without changing their ordering.. look at stability under either these learning, defining related notions (safe statistical knowledge), well measure verisimilitude model. prove number convergence results, showing how our track true probability after sampling, she eventually gains sense (statistical) knowledge probability. Finally, sketch contours dynamic doxastic logic learning.