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Building on previous work [4, 5] that bridged Formal Learning Theory and Dynamic Epistemic Logic in a topological setting, we introduce a Dynamic Logic for Learning Theory (DLLT), extending Subset Space Logics [17, 9] with dynamic observation modalities [o]ϕ, as well as with a learning operator L(#» o), which encodes the learner's conjecture after observing a finite sequence of data #» o. We completely axiomatise DLLT, study its expressivity and use it to characterise various notions of knowledge, belief, and learning.

We investigate the issues of inductive problem-solving and learning by doxastic agents. We provide topological characterizations of solvability and learnability, and we use them to prove that AGM-style belief revision is "universal", i.e., that every solvable problem is solvable by AGM conditioning.

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