Related papers: Jeffrey's rule of conditioning generalized to beli…

Jeffrey's rule has been generalized by Wagner to the case in which new evidence bounds the possible revisions of a prior probability below by a Dempsterian lower probability. Classical probability kinematics arises within this…

The conditioning in the Dempster-Shafer Theory of Evidence has been defined (by Shafer \cite{Shafer:90} as combination of a belief function and of an "event" via Dempster rule. On the other hand Shafer \cite{Shafer:90} gives a…

In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished,…

Conditioning is crucial in applied science when inference involving time series is involved. Belief calculus is an effective way of handling such inference in the presence of epistemic uncertainty -- unfortunately, different approaches to…

We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by…

This paper examines the concept of a combination rule for belief functions. It is shown that two fairly simple and apparently reasonable assumptions determine Dempster's rule, giving a new justification for it.

This paper examines the relationship between Shafer's belief functions and convex sets of probability distributions. Kyburg's (1986) result showed that belief function models form a subset of the class of closed convex probability…

Bayes's rule deals with hard evidence, that is, we can calculate the probability of event $A$ occuring given that event $B$ has occurred. Soft evidence, on the other hand, involves a degree of uncertainty about whether event $B$ has…

This paper describes a natural framework for rules, based on belief functions, which includes a repre- sentation of numerical rules, default rules and rules allowing and rules not allowing contraposition. In particular it justifies the use…

In this paper, we generalize the basic notions and results of Dempster-Shafer theory from predicates to formal concepts. Results include the representation of conceptual belief functions as inner measures of suitable probability functions,…

We are interested in the following version of Jeffreys's law: if two predictors are predicting the same sequence of events and either is doing a satisfactory job, they will make similar predictions in the long run. We give a classification…

The concept of updating a probability distribution in the light of new evidence lies at the heart of statistics and machine learning. Pearl's and Jeffrey's rule are two natural update mechanisms which lead to different outcomes, yet the…

In this paper we propose a new family of Belief Conditioning Rules (BCRs) for belief revision. These rules are not directly related with the fusion of several sources of evidence but with the revision of a belief assignment available at a…

Evidence in probabilistic reasoning may be 'hard' or 'soft', that is, it may be of yes/no form, or it may involve a strength of belief, in the unit interval [0, 1]. Reasoning with soft, [0, 1]-valued evidence is important in many situations…

In the canonical examples underlying Shafer-Dempster theory, beliefs over the hypotheses of interest are derived from a probability model for a set of auxiliary hypotheses. Beliefs are derived via a compatibility relation connecting the…

There are at least two ways to interpret numerical degrees of belief in terms of betting: (1) you can offer to bet at the odds defined by the degrees of belief, or (2) you can judge that a strategy for taking advantage of such betting…

This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely:…

We first show that there are practical situations in for instance forensic and gambling settings, in which applying classical probability theory, that is, based on the axioms of Kolmogorov, is problematic. We then introduce and discuss…

This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal…

Dempster/Shafer (D/S) theory has been advocated as a way of representing incompleteness of evidence in a system's knowledge base. Methods now exist for propagating beliefs through chains of inference. This paper discusses how rules with…