The motivation of possibility theory is to represent the imprecision intrinsic in natural language, in particular in expressions of the form x is R. A suitable topos of presheaves, i.e. an extension of classical set theory, is presented where sets of the form {x : x is R} can be constructed with x is R having the meaning given in possibility theory. The aim of the paper is to give an explicit m...

Possibilistic networks offer a qualitative approach for modeling epistemic uncertainty. Their practical implementation requires the specification of conditional possibility tables, as in the case of Bayesian networks for probabilities. This paper presents the possibilistic counterparts of the noisy probabilistic connectives (and, or, max, min, . . . ). Their interest is illustrated on an exampl...

We present a way of classifying the logically possible ways out of Gärdenfors’ inconsistency or triviality result on belief revision with conditionals. For one of these ways—conditionals which are not descriptive but which only have an inferential role as being given by the Ramsey test—we determine which of the assumptions in three different versions of Gärdenfors’ theorem turn out to be false....

1 Epistemic Possibility and Other Types of Possibility There is a lot that we don’t know. That means that there are a lot of possibilities that are, epistemically speaking, open. For instance, we don’t know whether it rained in Seattle yesterday. So, for us at least, there is an epistemic possibility where it rained in Seattle yesterday, and one where it did not. It’s tempting to give a very si...

The problem of expert opinions representation and aggregation has long been adressed in the only framework of probability theory. Nevertheless, recent years have witnessed many proposals in other uncertainty theories (possibility theory, evidence theory, imprecise probabilities). This paper casts the problem of aggregating expert opinions in a common underlying framework and shows how uncertain...

Possibilistic conditional independence is in­ vestigated : we propose a definition of this notion similar to the one used in probability theory. The links between independence and no-interactivity are investigated, and proper­ ties of these relations are given. The influ­ ence of the conjunction used to define a con­ ditional measure of possibility is also high­ lighted : we examine three types...

Recently, it has been emphasized that the possibility theory framework allows us to dis­ tinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinc­ tion may be useful when representing knowl­ edge, for modelling values which are not im­ possible because they are consistent with the available knowledge on the one ...

Causal theories of perception typically have problems in explaining deviant causal chains. They also have difficulty with other unusual putative cases of perception involving prosthetic aids, defective perception, scientifically extended cases of perception, and so on. But I show how a more adequate reflexive causal theory, in which objects or properties X cause a perceiver to acquire X-related...

In “standard” probability theory, one lists all events that are logically possible, and then places a normalized measure over them. This scheme is rather dry. It may happen that the list of possible events is encoded through logical sentences, and one must employ logical reasoning to determine which events are included in probabilistic assessments. It may also happen that probabilistic assessme...

Accepting truth-value realism can seem to raise an explanatory problem: what can explain our accuracy about mathematics, i.e., the match between human psychology and objective mathematical facts? A range of current truth-value realist philosophies of mathematics allow one to reduce this access problem to a problem of explaining our accuracy about which mathematical practices are coherent – in a...