Physical Possibility and Determinate Number Theory

Number Theory as the Ultimate Physical Theory ∗

At the Planck scale doubt is cast on the usual notion of space-time and one cannot think about elementary particles. Thus, the fundamental entities of which we consider our Universe to be composed cannot be particles, fields or strings. In this paper the numbers are considered as the fundamental entities.We discuss the construction of the corresponding physical theory. A hypothesis on the quant...

Possibility Theory Ii Conditional Possibility

It is shown that the notion of conditional possibility can be consistently introduced in possibility theory, in very much the same way as conditional expectations and probabilities are defined in the measureand integral-theoretic treatment of probability theory. I write down possibilistic integral equations which are formal counterparts of the integral equations used to define conditional expec...

Possibility Theory and the Risk

Possibility theory and statistical reasoning

Numerical possibility distributions can encode special convex families of probability measures. The connection between possibility theory and probability theory is potentially fruitful in the scope of statistical reasoning when uncertainty due to variability of observations should be distinguished from uncertainty due to incomplete information. This paper proposes an overview of numerical possi...

Integration in Possibility Theory

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...