Jan Cedervall: Para-consistent, doxastic hybrid logic

Abstract: In general choices are at least to some extent governed by expectations. While the world is consistent expectations about the world may be ambivalent or contain other para-consistencies. We hence argue that the normal Kripke axiom and necessitation are too strong for modelling expectations behind real-time choices where recovery from mistakes are impossible. Thus, weaker versions are suggested as a base for a para-consistent, doxastic hybrid logic, that still allows a relational semantics. Weaker axiom and the lack of full necessitation makes the logic deductively weaker. Model dynamics and logical induction are discussed, as ways to strengthen the weakened computational and concluding power.