Julien Rossit

Interval-based possibilistic logic

Possibilistic logic is a well-known framework for dealing with uncertainty and reasoning under inconsistent knowledge bases. Standard possibilistic logic expressions are propositional logic formulas associated with positive real degrees belonging to [0,1]. However, in practice it may be difficult for an expert to provide exact degrees associated with formulas of a knowledge base. This paper proposes a flexible representation of uncertain information where the weights associated with formulas are in the form of intervals. We first study a framework for reasoning with interval-based possibilistic knowledge bases by extending main concepts of possibilistic logic such as the ones of necessity and possibility measures. We then provide a characterization of an interval-based possibilistic logic base by means of a concept of compatible standard possibilistic logic bases. We show that interval-based possibilistic logic extends possibilistic logic in the case where all intervals are singletons. Lastly, we provide computational complexity results of deriving plausible conclusions from interval-based possibilistic bases and we show that the flexibility in representing uncertain information is handled without extra computational costs.

Min-based Assertional Merging Approach for Prioritized DL-Lite Knowledge Bases

DL-Lite is a powerful and tractable family of description logics specifically tailored for applications that use huge volumes of data. In many real world applications, data are often provided by several and potentially conflicting sources of information having different levels of priority. Possibility theory offers a very natural framework to deal with ordinal and qualitative uncertain beliefs or prioritized preferences. Thus, to encode prioritized assertional facts, a possibility DL-Lite logic is more suited. We propose in this paper a min-based assertional merging operator for possibilistic DL-Lite knowledge bases. We investigate in particular the situation where the sources share the same terminological base. We present a syntactic method based on conflict resolution which has a meaningful semantic counterpart when merging possibility distributions. We finally provide an analysis in the light of a new set of postulates dedicated to uncertain DL-Lite merging.

An Analysis of Sum-Based Incommensurable Belief Base Merging

Different methods have been proposed for merging multiple and potentially conflicting informations. Sum-based operators offer a natural method for merging commensurable prioritized belief bases. Their popularity is due to the fact that they satisfy the majority property and they adopt a non cautious attitude in deriving plausible conclusions. This paper analyses the sum-based merging operator when sources to merge are incommensurable, namely they do not share the same meaning of uncertainty scales. We first show that the obtained merging operator can be equivalently characterized either in terms of an infinite set of compatible scales, or by a well-known Pareto ordering on a set of models. We then study different families of compatible scales useful for merging process. This paper also provides a postulates-based analysis of our merging operators.

A max-based merging of incommensurable ranked belief bases based on finite scales

Recently, several approaches have been proposed to merge possibly contradictory belief bases. This paper focuses on max-based merging operators applied to incommensurable ranked belief bases. We first propose a characterization of a result of merging using Pareto-like ordering on a set of possible solutions. Then we propose two equivalent ways to recover the result of merging. The first one is based on the notion of compatible rankings defined on finite scales. The second one is only based on total pre-orders induced by ranked bases to merge.

A Polynomial Algorithm for Merging Lightweight Ontologies in Possibility Theory Under Incommensurability Assumption.

The context of this paper is the one of merging lightweight ontologies with prioritized or uncertain assertional bases issued from different sources. This is especially required when the assertions are provided by multiple and often conflicting sources having different reliability levels. We focus on the so-called egalitarian merging problem which aims to minimize the dissatisfaction degree of each individual source. The question addressed in this paper is how to merge prioritized assertional bases, in a possibility theory framework, when the uncertainty scales are not commensurable, namely when the sources do not share the same meaning of uncertainty scales. Using the notion of compatible scale, we provide a safe way to perform merging. The main result of the paper is that the egalitarian merging of prioritized assertional bases can be achieved in a polynomial time even if the uncertainty scales are not commensurable.

Rationalisation of Profiles of Abstract Argumentation Frameworks : Extended Abstract

We review a recently introduced model in which each of a number of agents is endowed with an abstract argumentation framework reflecting her individual views regarding a given set of arguments. A question arising in this context is whether the diversity of views observed in such a situation is consistent with the assumption that every individual argumentation framework is induced by a combination of, first, some basic factual information and, second, the personal preferences of the agent concerned. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. This is useful for understanding what types of profiles can reasonably be expected to occur in a multiagent system.

Rationalisation of Profiles of Abstract Argumentation Frameworks: Characterisation and Complexity

Different agents may have different points of view. Following a popular approach in the artificial intelligence literature, this can be modeled by means of different abstract argumentation frameworks, each consisting of a set of arguments the agent is contemplating and a binary attack-relation between them. A question arising in this context is whether the diversity of views observed in such a profile of argumentation frameworks is consistent with the assumption that every individual argumentation framework is induced by a combination of, first, some basic factual attack-relation between the arguments and, second, the personal preferences of the agent concerned regarding the moral or social values the arguments under scrutiny relate to. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. In doing so, we distinguish different constraints on admissible rationalisations, e.g., concerning the types of preferences used or the number of distinct values involved. We also distinguish two different semantics for rationalisability, which differ in the assumptions made on how agents treat attacks between arguments they do not report. This research agenda, bringing together ideas from abstract argumentation and social choice, is useful for understanding what types of profiles can reasonably be expected to occur in a multiagent system.

Merging interval-based possibilistic belief bases

In the last decade, several approaches were introduced in literature to merge multiple and potentially conflicting pieces of information. Within the growing field of application favourable to distributed information, data fusion strategies aim at providing a global and consistent point of view over a set of sources which can contradict each other. Moreover, in many situations, the pieces of information provided by these sources are uncertain. Possibilistic logic is a well-known powerful framework to handle such kind of uncertainty where formulas are associated with real degrees of certainty belonging to [0,1]. Recently, a more flexible representation of uncertain information was proposed, where the weights associated with formulas are in the form of intervals. This interval-based possibilistic logic extends classical possibilistic logic when all intervals are singletons, and this flexibility in representing uncertain information is handled without extra computational costs. In this paper, we propose to extend a well known approach of possibilistic merging to the notion of interval-based possibilistic knowledge bases. We provide a general semantic approach and study its syntactical counterpart. In particular, we show that convenient and intuitive properties of the interval-based possibilistic framework hold when considering the belief merging issue.