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...

— 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...

Materialism is the idea that human beings are material objects—brains, perhaps, or some part of the brain—without immaterial selves or souls. I give two arguments against materialism. The first is an argument from possibility: it is possible that I should exist when no part of my body exists, in which case I am not identical with my body or any part of my body. The second is an argument from im...

This paper presents the extension of results on reasoning with totally ordered belief bases to the partially ordered case. The idea is to reason from logical bases equipped with a partial order expressing relative certainty and to construct a partially ordered deductive closure. The difficult point lies in the fact that equivalent definitions in the totally ordered case are no longer equivalent...

It often happens that different references (i.e. data descriptions), possibly coming from different heterogeneous data sources, concern the same real world entity. In such cases, it is necessary: (i) to detect, through reconciliation methods, whether different data descriptions refer to the same real world entity and (ii) to fuse them into a unique representation. Here we assume the reference r...

In this paper, we study the semantics for the logics of preference based on possibility theory. Possibility distributions representing the preference between worlds are associated with the possible world models for dynamic logics. Then the preference between actions are determined by comparing some measures of their consequences. We will define different logics of preference by considering the ...