4 research outputs found
On the Modal Logic of Jeffrey Conditionalization
We continue the investigations initiated in the recent papers \cite{BGyR,GyBLst} where Bayes logics have been introduced to study the general laws of Bayesian belief revision. In Bayesian belief revision a Bayesian agent revises (updates) his prior belief by conditionalizing \ud
the prior on some evidence using the Bayes rule. In this paper we take the more general Jeffrey formula as a conditioning device and study the corresponding modal logics that we call Jeffrey logics, focusing mainly on the countable case. The containment relations among \ud
these modal logics are determined and it is shown that the logic of Bayes and Jeffrey updating are very close. It is shown that the modal logic of belief revision determined by probabilities on a finite or countably infinite set of elementary propositions is {\em not finitely axiomatizable}.\ud
The significance of this result is that it clearly indicates that axiomatic approaches to belief revision might be severely limited
Data Obsolescence Detection in the Light of Newly Acquired Valid Observations
The information describing the conditions of a system or a person is
constantly evolving and may become obsolete and contradict other information. A
database, therefore, must be consistently updated upon the acquisition of new
valid observations that contradict obsolete ones contained in the database. In
this paper, we propose a novel approach for dealing with the information
obsolescence problem. Our approach aims to detect, in real-time, contradictions
between observations and then identify the obsolete ones, given a
representation model. Since we work within an uncertain environment
characterized by the lack of information, we choose to use a Bayesian network
as our representation model and propose a new approximate concept,
-Contradiction. The new concept is parameterised by a confidence
level of having a contradiction in a set of observations. We propose a
polynomial-time algorithm for detecting obsolete information. We show that the
resulting obsolete information is better represented by an AND-OR tree than a
simple set of observations. Finally, we demonstrate the effectiveness of our
approach on a real elderly fall-prevention database and showcase how this tree
can be used to give reliable recommendations to doctors. Our experiments give
systematically and substantially very good results
The modal logic of Bayesian belief revision
In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable