The Review of Symbolic Logic

Research Article

SOME COMPLETENESS THEOREMS IN THE DYNAMIC DOXASTIC LOGIC OF ITERATED BELIEF REVISION

KRISTER SEGERBERGa1 c1*

a1 Philosophy Department, Uppsala University

Abstract

The success of the AGM paradigm—the theory of belief change initiated by Alchourrón, Gärdenfors, and Makinson—is remarkable, as even a quick look at the literature it has generated will testify. But it is also remarkable, at least in hindsight, how limited was the original effort. For example, the theory concerns the beliefs of just one agent; all incoming information is accepted; belief change is uniquely determined by the new information; there is no provision for nested beliefs. And perhaps most surprising: there is no analysis of iterated change.

In this paper it is that last restriction that is at issue. Our medium of study is dynamic doxastic logic (DDL). The success of the AGM paradigm The particular contribution of the paper is detailed completeness proofs for three dynamic doxastic logics of iterated belief revision.

The problem of extending the AGM paradigm to include iterated change has been discussed for years, but systematic discussions have appeared only recently (see Segerberg, 2007 and forthcoming, but also van Benthem, 2007; Rott, 2006; Zvesper, 2007).

(Received June 26 2008)

Correspondence:

c1 PHILOSOPHY DEPARTMENT, BOX 627, S-751 26 UPPSALA, SWEDEN E-mail: krister.segerberg@filosofi.uu.se

Footnotes

* Most of the research reported in this paper was carried out during autumn 2006 when the author was a fellow-in-residence at NIAS (the Netherlands Institute of Advanced Study, Wassenaar). The paper was modified in 2009 in the light of a very helpful report by a referee who spotted an error in a previous draft. The error is corrected here, but unfortunately it also occurs in some already published papers, notably Segerberg (2001). (See Footnote 5.)