This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the available information concerning the value of a logical or numerical variable is represented by a possibility distribution which restricts its more or less po...

Possibilistic logic is an important uncertainty reasoning mech anism based on Zadeh s possibility theory and classical logic The deduc tion rules of possibilistic logic have been obtained from classical resolu tion rule by attaching possibility or necessity weight to ordinary clauses However since not all possibility valued formulae can be converted into equivalent possibilistic clauses the res...

The probabilistic Noisy OR model has been widely used as a means of reducing the amount of probabilistic information that is needed to specify the interaction between groups of variables. Motivated by our work on the diagnosis of faults in satellite subsystems , which required a similar synthesis of partial possibilistic information on interactions , we consider a number of ways of gener-alisin...

This paper is a reply to Laviolette and Seaman’s critical discussion of fuzzy set theory. Rather than questioning the interest of the Bayesian approach to uncertainty, some reasons why Bayesian find the idea of a fuzzy set not palatable are laid bare. Some links between fuzzy sets and probability that Laviolette and Seaman seem not to be aware of are pointed out. These links suggest that, contr...

This paper presents further work on a 3D visualisation system for the reconstruction of historical structures which takes into account archaeological uncertainty. The uncertainty associated with an archaeologist’s interpretation is represented using possibility theory and visualised by shader-based information visualisation schemes. An increase or decrease in uncertainty is influenced by any re...

In this paper we develop a bimodal perspective on possibility semantics, a framework allowing partiality of states that provides an alternative modeling for classical propositional and modal logics [Humberstone, 1981, Holliday, 2015a]. In particular, we define a full and faithful translation of the basic modal logic K over possibility models into a bimodal logic of partial functions over partia...

Doubts about a maxim like Hume’s have a variety of historical sources. Some date back as far as Descartes’s claim that, since he can conceive himself in a purely mental condition, his essence is only to think. “How does it follow,” Arnauld asks, “from the fact that he is aware of nothing else belonging to his essence, that nothing else does in fact belong to it?” Others are as recent as the dis...

This paper explores the existing relationship between Possibility Theory and Theory of Evidence, when they are both applied to fuzzy arithmetic. Possibility Theory arithmetic is based on the extension principle (projection of the joint possibility distribution), while in Theory of Evidence, the consonant bodies of evidence obtained from each operand are combined into a new joint body of evidenc...

QCD sheds considerable light on several of the most basic features of the natural world including the origin of mass, the feebleness of gravity, the extent to which the properties of matter can be determined conceptually, the possible utility of the anthropic principle, and the metatheoretic notions of effectiveness and computability. I discuss these applications here. Contemporary academic or ...