Valuation-based systems (VBS) can be considered as a generic uncertainty framework that has many uncertainty calculi, such as probability theory, a version of possibility theory where combination is the product t-norm, Spohn’s epistemic belief theory, and DempsterShafer belief function theory, as special cases. In this paper, we focus our attention on conditioning, which is defined using the co...

This paper motivates the study of counterpossibles (logically impossible counterfactuals) as necessary for developing a decision theory suitable for generally intelligent agents embedded within their environments. We discuss two attempts to formalize a decision theory using counterpossibles, one based on graphical models and another based on proof search.

In the last dozen years or so, our understanding of modality has been much improved by means of possible-world semantics: the project of analyzing modal language by systematically specifying the conditions under which a modal sentence is true at a possible world. I hope to do the same for counterfactual conditionals. I write A [5]-~ C for the counter-factual conditional with antecedent A and co...

In 1987 Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. In 2001 Carlsson and Fullér defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions, and they introduced the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions, which ar...

The possibility for the occurrence in crystals of a phenomenon, resembling turbulence, is discussed. This phenomenon, called heterophase turbulence, is manifested by the fluctuational appearance inside a crystalline sample of disordered regions randomly distributed in space. The averaged picture for such a turbulent solid is exemplified by an exactly solvable lattice-gas model. The origin of he...

Modern science has undermined belief in countless imaginary causalities. What is the nature of the relation between mind and brain? Philosophers have debated the issue for millennia, but it is only in the last twenty years that empirical evidence has begun to uncover some of the secrets of this ancient riddle. This lecture explores the possiblity that advances in neuroscience will undermine and...

The paper discusses integration in possibility theory, both in an ordinal and in a numerical (behavioral) context. It is shown that in an ordinal context, the fuzzy integral has an important part in at least three areas: the extension of possibility measures to larger domains, the construction of product measures from marginals and the definition of conditional possibilities. In a numerical (be...

We consider the possibility problem of determining if a document is a possible world of a probabilistic document, in the setting of probabilistic XML. This basic question is a special case of query answering or tree automata evaluation, but it has specific practical uses, such as checking whether an user-provided probabilistic document outcome is possible or sufficiently likely. In this paper, ...

We generalize permissibility (Brandenburger, 1992) to allow for any suitably defined model of preference and definition of possibility. We also prove that the generalized solution concept characterizes rationality, caution, and common “belief” of rationality and caution. JEL classification: C72; D81