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- Peter Walley
- Artif. Intell.
- 1996

- Peter Walley
- Int. J. Approx. Reasoning
- 1999

Belief functions, possibility measures and Choquet capacities of order 2, which are special kinds of coherent upper or lower probability, are amongst the most popular mathematical models for uncertainty and partial ignorance. I give examples to show that these models are not sufficiently general to represent some common types of uncertainty. Coherent lower… (More)

- Fábio Gagliardi Cozman, Peter Walley
- ISIPTA
- 2001

This paper investigates Walley's concepts of epistemic irrelevance and epistemic independence for imprecise probability models. We study the mathematical properties of irrelevance and independence, and their relation to the graphoid axioms. Examples are given to show that epistemic irrelevance can violate the symmetry, contraction and intersection axioms,… (More)

- Inés Couso, Serafín Moral, Peter Walley
- ISIPTA
- 1999

In this paper we try to clarify the notion of independence for imprecise probabilities. Our main point is that there are several possible definitions of independence which are applicable in different types of situation. With this aim, simple examples are given in order to clarify the meaning of the different concepts of independence and the relationships… (More)

- Peter Walley, Gert de Cooman
- Int. J. Approx. Reasoning
- 1999

Possibility measures and conditional possibility measures are given a behavioural interpretation as marginal betting rates against events. Under this interpretation, possibility measures should satisfy two consistency criteria, known asàvoiding sure loss' and`coherence'. We survey the rules that have been proposed for deening conditional possibilities and… (More)

- PETER WALLEY
- 1998

This is an introduction to the concepts of lower and upper prevision and the mathematical theory of coherence. Upper and lower previsions are generalisations of upper and lower probabilities. They can model a very wide variety of kinds of uncertainty, partial information and ignorance. The theory of coherent lower previsions is based on a simple behavioural… (More)

We solve two fundamental problems of probabilistic reasoning: given a finite set of conditional probability assessments, how to determine whether the assessments are mutually consistent, and how to determine what they imply about the conditional probabilities of new events? These problems were posed in 1854 by George Boole, who gave a partial solution using… (More)

- PETER WALLEY
- 1998

The paper discusses the problem of modelling linguistic uncertainty, which is the uncertainty produced by statements in natural language. For example, the vague statement`Mary is young' produces uncertainty about Mary's age. We concentrate on simple aarmative statements of the typèsubject is predicate', where the predicate satisses a special condition… (More)

- Peter Walley, Serafõ Ân Moral
- 1997

In the problem of parametric statistical inference with a ®nite parameter space, we propose some simple rules for de®ning posterior upper and lower probabilities directly from the observed likelihood function, without using any prior information. The rules satisfy the likelihood principle and a basic consistency principle (`avoiding sure loss'), they… (More)

- Peter Walley, Gert de Cooman
- Inf. Sci.
- 2001

1.1 INTRODUCTION Information is commonly transmitted through statements in natural language. The statement 'Mary is young', for instance, provides partial information about Mary's age. If initially we know nothing about Mary's age and we subsequently hear that she is young, our knowledge about her age has increased, although we remain uncertain about her… (More)