Arbitrary Radical Upgrades

Raul Fervari, Benjamin Icard

Abstract: This paper presents and investigates \(\textsf{ARUL} \), a variant of dynamic belief revision logic in which revision policies, in particular radical, or lexicographic, upgrades, can be arbitrary. We discuss the motivations of having this kind of soft arbitrary operator, concretely for refining the analysis of agentivity and modelling classical epistemic paradoxes. We introduce a sound and complete axiomatic system over models whose accessibility relation is a reflexive, transitive and locally connected pre-order, following an approach parallel to Arbitrary Public Announcement Logic (\(\textsf{APAL} \)) for proving completeness.