Can doxastic agents learn? On the temporal structure of learning
Cédric. Dégremont, Nina Gierasimczuk
Abstract:
We analyse learning as the process of conjecture-change over
time. Treating ``conjectures'' as beliefs, we link the process of
conjecture-change to doxastic update. Using this approach, we
reconstruct and analyse the temporal aspect of learning in the limit
in the context of temporal and dynamic logics of belief change. We
propose a reduction of the learnability task to a generalized problem
of DETL model checking. Furthermore, we prove a DETL representation
result corresponding to an important theorem from Learning Theory,
that characterizes learnability, namely Angluin's theorem. We also
place notions of learning theory and doxastic temporal logic in a
common perspective in order to compare them. We focus both on the
properties of agents and fine-grained notions of belief and
knowledge. Finally, we consider an extension of the classical learning
theoretic framework by introducing more agents and extending the
protocols to include a possibility of communication between the
agents.
Keywords: formal learning theory; dynamic epistemic logic; doxastic temporal logic; identification in the limit; protocols