Dynamic epistemic logic for implicit and explicit beliefs

The dynamic turn in Epistemic Logic is based on the idea that notions of information should be studied together with the actions that modify them. Dynamic epistemic logics have explored how knowledge and beliefs change as consequence of, among others, acts of observation and upgrade. Nevertheless, the omniscient nature of the represented agents has kept finer actions outside the picture, the most important being the action of inference. Following proposals for representing non-omniscient agents, recent works have explored how implicit and explicit knowledge change as a consequence of acts of observation, inference, consideration and even forgetting. The present work proposes a further step towards a common framework for representing finer notions of information and their dynamics. We propose a combination of existing works in order to represent implicit and explicit beliefs. Then, after adapting definitions for the actions of upgrade and retraction, we discuss the action of inference on beliefs, analyzing its differences with respect to inference on knowledge and proposing a rich system for its representation.