129,480 research outputs found
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
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
Matricial circular systems and random matrices
We introduce and study `matricial circular systems' of operators which play
the role of matricial counterparts of circular operators. They describe the
asymptotic joint *-distributions of blocks of independent block-identically
distributed Gaussian random matrices with respect to partial traces. Using
these operators, we introduce `circular free Meixner distributions' as the
non-Hermitian counterparts of free Meixner distributions and construct for them
a random matrix model. Our approach is based on the concept of matricial
freeness applied to operators on Hilbert spaces. It is closely related to
freeness with amalgamation over the algebra A of r x r diagonal matrices
applied to operators on Hilbert A-bimodules.Comment: 27 pages, major revision, results on the relation to operator-valued
free probability are ne
Belief revision in the propositional closure of a qualitative algebra
Belief revision is an operation that aims at modifying old be-liefs so that
they become consistent with new ones. The issue of belief revision has been
studied in various formalisms, in particular, in qualitative algebras (QAs) in
which the result is a disjunction of belief bases that is not necessarily
repre-sentable in a QA. This motivates the study of belief revision in
formalisms extending QAs, namely, their propositional clo-sures: in such a
closure, the result of belief revision belongs to the formalism. Moreover, this
makes it possible to define a contraction operator thanks to the Harper
identity. Belief revision in the propositional closure of QAs is studied, an
al-gorithm for a family of revision operators is designed, and an open-source
implementation is made freely available on the web
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