Belief Changes and Cognitive Development: Doxastic Logic $${\mathsf {LCB}}$$
Marcin Łyczak · Axiomathes · 2020
Abstract We present the logic $${\mathsf {LCB}}$$ LCB which is expressed in a propositional language constantly enriched by new atomic expressions. Our formal framework is the propositional doxastic logic $${\mathsf {KD45}}$$ KD45 with the belief operator $${\mathcal {B}}$$ B , extended by the $${\mathcal {C}}$$ C operator, to be readit changes that .... We describe the changing beliefs of an agent who uses progressively expanding language. The approach presented here allows us to weaken pragmatic objections to the so-called principle ofnegative retrospectionaccepted in $${\mathsf {KD45}}$$ KD45 and the problem oflogical omniscience. In what follows, we present the expanding propositional language used in our formalism, interpreted using an epistemic version of Kripke semantics. Next, we give a syntactic characterization of logic $${\mathsf {LCB}}$$ LCB and prove the soundness and completeness of $${\mathsf {LCB}}$$ LCB in respect to our semantics. Finally, we compare the idea of expanding language with the notion ofagent awarenessand we relate our formalism to two epistemic temporal logics.