Igor Sedlár (Institute of Philosophy, Deparment of Logic):
This One Sparks Joy: De-cluttering Belief Bases with Relevant Epistemic Logic
Classical epistemic logic imposes various closure properties on the agent's belief set. Some of these principles, such as closure under Ex Contradictione Quodlibet, require the agent to clutter their belief base with irrelevant consequences of their beliefs. We set up a framework for epistemic logic overcoming the problem of irrelevant closure. In our framework, the agent is modeled as reasoning in accordance with relevant logic. At the same time, however, the logics generated by this framework extend classical propositional logic -- relevant logic is committed to the scope of modal operators, so to speak. Our main technical result is a modular completeness theorem. We also present an extension of the framework that expresses the distinction between explicit belief and implicit belief where the latter is represented as classical closure of explicit belief. The talk is based on joint work with Pietro Vigiani.