Revising Typical Beliefs: One Revision to Rule Them All

Propositional Typicality Logic (PTL) extends propositional logic with a connective • expressing the most typical (alias normal or conventional) situations in which a given sentence holds. As such, it generalises e.g.~preferential logics that formalise reasoning with conditionals such as ``birds typically fly''. In this paper, we study revision of sets of PTL-sentences. We first show why it is necessary to extend the PTL-language with a possibility operator, and then define the revision of PTL-sentences syntactically and characterise it semantically. We show that this allows us to represent a wide variety of existing revision methods, such as propositional revision and revision of epistemic states. Furthermore, we provide several examples showing why our approach is innovative. In more detail, we study revision of a set of conditionals under preferential closure, and the addition and contraction of possible worlds from an epistemic state.