# Dynamic Descriptors

• Sven Ove Hansson
Chapter
Part of the Trends in Logic book series (TREN, volume 46)

## Abstract

A dynamic descriptor carries information on how an agent’s beliefs are disposed to be changed in response to potential input(s). A particularly important class of dynamic descriptors are the Ramsey descriptors that have the form $$\Psi \Rightarrow \Xi$$ where $$\Psi$$ and $$\Xi$$ are (static) descriptors of the types introduced in Chapter . For example, $$\mathfrak {B}(p \vee q) \Rightarrow \lnot \mathfrak {B}r$$ denotes that if the agent changes her beliefs to believe that $$p \vee q$$, then she will not believe in r. Ramsey descriptors are axiomatically characterized with a set of plausible postulates that are generalizations of postulates commonly used in the logic of conditional sentences. It is also shown that Ramsey descriptors can unproblematically be inserted into belief sets. Revision by Ramsey descriptors does not give rise to the problems that arise when Ramsey test conditionals are inserted into the AGM framework or related models of belief change. The special case represented by the Ramsey descriptor $$\mathfrak {B}p \Rightarrow \mathfrak {B}q$$ corresponds to standard Ramsey test conditionals, and we can define the epistemic conditional $$p \rightarrowtail q$$ (“if p then q”) to hold if and only if $$\mathfrak {B}p \Rightarrow \mathfrak {B}q$$. However, this is not the only way to derive a sentential conditional from a Ramsey descriptor. Two alternatives to the standard approach are introduced. Furthermore, a formula for deriving non-monotonic inference from a Ramsey descriptor is presented. This proposal is offered as an improvement over the common view that the logic of non-monotonic inference is a fragment of the logic of conditional sentences. The chapter also explores various methods to introduce modalities and autoepistemic beliefs into the belief change framework. The introduction of modalities serves to connect descriptor revision with Dynamic Doxastic Logic (DDL) and related systems.