29,058 research outputs found
Extending the Harper Identity to Iterated Belief Change
The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators
A characterization of sequential equilibrium in terms of AGM belief revision
In [G. Bonanno, Rational choice and AGM belief revision, Artificial Intelligence, 2009] a semantics for one-stage AGM belief revision was proposed based on choice frames, borrowed from the rational choice literature. In this paper we extend the semantics of choice frames to deal with iterated belief revision and use the corresponding structures to analyze extensive-form games. Choice frames can be used to represent a player's initial beliefs and disposition to change those beliefs when informed that it is her turn to move. If the frame satisfies AGM-consistency and a natural postulate for iterated belief revision, then it is rationalizable by a total pre-order on the set of histories. We show that three properties of this total pre-order, together with the hypothesis of agreement among players, provide a characterization of the notion of consistent assessment, which is the central component of the notion of sequential equilibrium proposed by Kreps and Wilson [Econometrica, 1982].Choice function, AGM belief revision, extensive-form game, sequential equilibrium, iterated belief revision, backward induction.
Decrement Operators in Belief Change
While research on iterated revision is predominant in the field of iterated
belief change, the class of iterated contraction operators received more
attention in recent years. In this article, we examine a non-prioritized
generalisation of iterated contraction. In particular, the class of weak
decrement operators is introduced, which are operators that by multiple steps
achieve the same as a contraction. Inspired by Darwiche and Pearl's work on
iterated revision the subclass of decrement operators is defined. For both,
decrement and weak decrement operators, postulates are presented and for each
of them a representation theorem in the framework of total preorders is given.
Furthermore, we present two sub-types of decrement operators
Belief change in branching time: AGM-consistency and iterated revision
We study belief change branching-time structures. First, we identify a property of branching-time frames that is equivalent to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in [Bonanno, Axiomatic characterization of the AGM theory of belief revision in a temporal logic, Artificial Intelligence, 2007]. Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically.iterated belief revision, branching time, information, belief, modal logic, AGM belief revision
An Investigation of Darwiche and Pearl's Postulates for Iterated Belief Update
Belief revision and update, two significant types of belief change, both
focus on how an agent modify her beliefs in presence of new information. The
most striking difference between them is that the former studies the change of
beliefs in a static world while the latter concentrates on a
dynamically-changing world. The famous AGM and KM postulates were proposed to
capture rational belief revision and update, respectively. However, both of
them are too permissive to exclude some unreasonable changes in the iteration.
In response to this weakness, the DP postulates and its extensions for iterated
belief revision were presented. Furthermore, Rodrigues integrated these
postulates in belief update. Unfortunately, his approach does not meet the
basic requirement of iterated belief update. This paper is intended to solve
this problem of Rodrigues's approach. Firstly, we present a modification of the
original KM postulates based on belief states. Subsequently, we migrate several
well-known postulates for iterated belief revision to iterated belief update.
Moreover, we provide the exact semantic characterizations based on partial
preorders for each of the proposed postulates. Finally, we analyze the
compatibility between the above iterated postulates and the KM postulates for
belief update
Iterated belief change: the case of expansion into inconsistency
Constructing models that allow iterated changes
is one of the most studied problems in the literature on belief
change. However, up to now, iteration of expansion was only
studied as a special case of consistent revision and, as far
we know, there is no work in the literature that deals with
expansions into inconsistency in a supraclassical framework.
In this paper, we provide a semantics for iterated expansion, as
well as its axiomatic characterization. We extend the model to
two well-known families of iterated belief change (natural and
lexicographic). Iteration of expansion can be combined with
existent models of iteration of revision and contraction. Since
we are able to accommodate different inconsistent belief states,
iteration of expansion allows us to define new belief change
functions that are currently only defined for belief bases: semi revision, external revision, as well as consolidation.info:eu-repo/semantics/publishedVersio
Iterated Belief Change and the Levi Identity
Most works on iterated belief change have focussed on iterated belief revision, namely, on how to compute (K star x) star y. However, historically, belief revision has been defined in terms of belief expansion and belief contraction that have been viewed as primary operations. Accordingly, what we should be looking at are constructions like: (K+x)+y, (K-x)+y, (K-x)+y and (K-x)-y. The first two constructions are relatively innocuous. The last two are, however, more problematic. We look at these sequential operations. In the process, we use the Levi Identity as the guiding principle behind state changes (as opposed to belief set changes)
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