Special Session LIRa Seminar on Learning, Explicit Beliefs and Temporal Representations

Probabilistic conditioning, also known as Bayesian update, is the standard learning method in the Bayesian approach to learning and belief change. A number of different qualitative analogues of this method have been proposed in Belief Revision theory (conditioning, lexicographic revision, minimal revision) and Dynamic Epistemic Logic (update, radical upgrade, conservative upgrade). We investigate all these (probabilistic and qualitative) methods from a Learning Theory perspective, considering the question whether any of them is “universal” (i.e. as good at tracking the truth as any other learning method). We show that this is not the case, as long as we keep the standard probabilistic (or belief-revision) setting. On the positive side, we show that if we consider appropriate generalizations of conditioning in a non-standard, non-wellfounded setting, then universality is achieved. (joint work with Nina Gierasimczuk and Sonja Smets)

What are the epistemic temporal properties characterizing DEL updates? We discuss to what extent the answer is dependent on an underlying notion of informational equivalence. (joint and ongoing work with Tomohiro Hoshi, Benedikt Löwe and Andreas Witzel)

Recent dynamic epistemic logics have explored how the notions of knowledge and beliefs (among others) change as consequence of diverse acts of observation and diverse forms of revision (among many others). Nevertheless, the omniscient nature of the represented agents has kept finer actions outside the picture. Following proposals for representing non-omniscient agents, recent works have explored how acts of inference, consideration and forgetting affect an agent’s implicit and explicit *knowledge*. The present work focusses on acts that affect the notions of implicit and explicit *beliefs*. We propose a representation of these notions based on existing proposals for representing implicit/explicit knowledge and for representing beliefs. Then we look into their dynamics, first by adapting the existing notion of belief revision to our non-omniscient setting, and then by introducing a rich framework that allow us to represent diverse forms of inference that involve not only knowledge but also beliefs. Finally we briefly discuss how some forms of default and abductive reasoning can be represented in the framework.