Irrevocable Belief Revision in Dynamic Doxastic Logic

AbstractI propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided.

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

The Review of Symbolic Logic ◽

10.1017/s1755020309990384 ◽

2010 ◽

Vol 3 (2) ◽

pp. 228-246 ◽

Cited By ~ 4

Author(s):

KRISTER SEGERBERG

Keyword(s):

Belief Revision ◽

Belief Change ◽

Doxastic Logic ◽

New Information ◽

Incoming Information ◽

Iterated Belief Revision ◽

Dynamic Doxastic Logic ◽

Completeness Theorems ◽

Nested Beliefs

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).

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