Can Doxastic Agents Learn? On the Temporal Structure of Learning

Formal learning theory formalizes the phenomenon of language acquisition. The theory focuses on various properties of the process of conjecture-change over time, and therefore it is also applicable in philosophy of science, where it can be interpreted as a theory of empirical inquiry. Treating "conjectures" as beliefs, we link the process of conjecture-change to doxastic update. Using this approach, we reconstruct and analyze the temporal aspect of learning in the context of temporal and dynamic logics of belief change. We provide a translation of learning scenarios into the domain of dynamic doxastic epistemic logic. Then, we express the problem of finite identifiability as a problem of epistemic temporal logic model checking. Furthermore, we prove a doxastic epistemic temporal logic representation result corresponding to an important theorem from learning theory, that characterizes identifiability in the limit, namely Angluin's theorem. In the end we discuss consequences and possible extensions of our work.