There are two readings of a possibility distribution, a representation format which is useful for encoding uncertain knowledge or preferences. The negative information reading, based on possibility and necessity measures, emphasizes the fact that some interpretations are impossible, or at least have an upper-bounded possibility level. The positive information reading points out that possibility...

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability theory, and the two others are based on the notion of conditional possibility. These two have enough expressive power to support the whole possibility theory, an...

We give a generalization of possibility and necessity measures: their domains are extended towards fields of sets, and their codomains towards arbitrary complete lattices. In this way, these measures can be associated with (Q,≤)-fuzzy sets, where (Q,≤) is at least a poset. An important inconsistency problem, intricately linked with this association, is solved. It is argued that order lies at th...

In this paper we study how the framework of Petri nets can be extended and applied to study recurrent events. We use possibility theory to realistically model temporal properties of the recurrent processes being modeled by an extended Petri net. Such temporal properties include timestamps stored in tokens and durations of firing the transitions. We apply our method to model the recurrent behavi...

In the last years, the Authors have proposed the use of the Random-Fuzzy Variables (RFVs) to represent measurements results. An RFV is an extension of a fuzzy variable, which is the natural variable in the mathematical possibility theory (in the same way the random variable is the natural variable in the probability theory). The aim of this presentation is to show, through a remotely controlled...

I argue that the thesis that time travel is logically possible, is inconsistent with the necessary truth of any of the usual ‘open future-objective present’ models of the universe. It has been relatively uncontroversial until recently to hold that presentism is inconsistent with the possibility of time travel. I argue that recent arguments to the contrary do not show that presentism is consiste...

In a series of studies children show increasing mastery of irregular plural forms (such as mice) simply by producing erroneous over-regularized versions of them (such as mouses). We explain this phenomenon in terms of successive approximation in imitation: Children over-regularize early in acquisition because the representations of frequent, regular plural forms develop more quickly, such that ...

— In this paper we study the optimal saving problem in the framework of possibility theory. The notion of possibilistic precautionary saving is introduced as a measure of the way the presence of possibilistic risk (represented by a fuzzy number) influences a consumer in establishing the level of optimal saving. The notion of prudence of an agent in the face of possibilistic risk is defined and ...

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 scale only , and another based on product, for which a richer structure is needed, and which is a particular case of Dempster's rule of conditioning . Besides...

In this paper formal properties of CI in diierent frameworks are studied. The rst part is devoted to the comparison of three diierent frameworks for study CI: probability theory, theory of relational databases and Spohn's theory of ordinal conditional functions. Although CI{models arising in these frameworks are very similar (they satisfy semigraphoid axioms) we give examples showing that their...