9,905 research outputs found
On Strengthening the Logic of Iterated Belief Revision: Proper Ordinal Interval Operators
Darwiche and Pearlās seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of āreductionismā that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka āIndependenceā, characteristic of āadmissibleā operators, remain commendably more modest. In this paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern
the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a āproper ordinal intervalā (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general
A Conditional Logic for Iterated Belief Revision
In this paper we (Laura Giordano, Nicola Olivetti and myself) propose a conditional logic to represent iterated belief revision systems. We propose a set of postulates for belief revision which are a small variant of Darwiche and Pearl's ones.The resulting conditional logic has a standard semantics in terms of selection function models, and provides a natural representation of epistemic states. A Representation Theorem establishes a correspondence between iterated belief revision systems and conditional models. Our Representation Theorem does not entail GƤrdenfors' Triviality Result
On strengthening the logic of iterated belief revision: proper ordinal interval operators
Darwiche and Pearlās seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. However, most of the suggestions for doing so have been radical enough to result in a dubious āreductionistā principle that identiļ¬es belief states with orderings of worlds. The present paper oļ¬ers a more modest strengthening of Darwiche and Pearlās proposal. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles govern the relation between two posterior conditional belief sets obtained from a common prior by diļ¬erent revisions. We show that operators from the family that these principles characterise, which subsumes both lexicographic and restrained revision, can be represented as relating belief states that are associated with a āproper ordinal intervalā assignment, a structure more ļ¬ne-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of a large number of AGM era postulates
On strengthening the logic of iterated belief revision: Proper ordinal interval operators
Darwiche and Pearlās seminal 1997 article outlined a number
of baseline principles for a logic of iterated belief revision.
These principles, the DP postulates, have been supplemented
in a number of alternative ways. Most suggestions have resulted
in a form of āreductionismā that identifies belief states
with orderings of worlds. However, this position has recently
been criticised as being unacceptably strong. Other proposals,
such as the popular principle (P), aka āIndependenceā, characteristic
of āadmissibleā operators, remain commendably more
modest. In this paper, we supplement the DP postulates and
(P) with a number of novel conditions. While the DP postulates
constrain the relation between a prior and a posterior
conditional belief set, our new principles notably govern
the relation between two posterior conditional belief sets obtained
from a common prior by different revisions. We show
that operators from the resulting family, which subsumes both
lexicographic and restrained revision, can be represented as
relating belief states associated with a āproper ordinal intervalā
(POI) assignment, a structure more fine-grained than a
simple ordering of worlds. We close the paper by noting that
these operators satisfy iterated versions of many AGM era
postulates, including Superexpansion, that are not sound for
admissible operators in general
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