Sylvain Lagrue

Reasoning with Partially Ordered Information in a Possibilistic Logic Framework

In many applications, the reliability relation associated with available information is only partially defined, while most of existing uncertainty frameworks deal with totally ordered pieces of knowledge. Partial pre-orders offer more flexibility than total pre-orders to represent incomplete knowledge. Possibilistic logic, which is an extension of classical logic, deals with totally ordered information. It offers a natural qualitative framework for handling uncertain information. Priorities are encoded by means of weighted formulas, where weights are lower bounds of necessity measures. This paper proposes an extension of possibilistic logic for dealing with partially ordered pieces of knowledge. We show that there are two different ways to define a possibilistic logic machinery which both extend the standard one.

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.

Interval-Based Possibilistic Networks

In this paper, we study foundations of interval-based possibilistic networks where possibility degrees associated with nodes are no longer singletons but sub-intervals of [0,1]. This extension allows to compactly encode and reason with epistemic uncertainty and imprecise beliefs as well as with multiple expert knowledge. We propose a natural semantics based on compatible possibilistic networks. The last part of the paper shows that computing the uncertainty bounds of any event can be computed in interval-based networks without extra computational cost with respect to standard possibilistic networks.

Methods Handling Accident and Traffic Jam Information with Belief Functions in VANETs

In this paper, different methods using belief functions are proposed to share and manage information about local and spatial events on the road in V2V communications. In order to take into account messages ageing, a reinforcement mechanism considering that events disappear over the time is compared to the discounting mechanism. Two strategies for messages management are also emphasized: a first one where each message is stored and sent when possible and a second one where only fused messages are considered. Presented work shows how results can be upgraded when considering the world update, especially for dynamic events. Finally, an influence mechanism is introduced for traffic jam events to smooth and improve results when vehicles receive information about only some parts of the road.

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.

Belief revision of GIS systems: the results of REV!GIS

This paper presents a synthesis of works performed on the practical tractability of revision on geographic information within the european REV!GIS project.It surveys di.erent representations of the revision problem as well as di.erent implementations of the adopted stategy: Removed Set Revision (RSR). A comparison of the representation formalisms is provided, a formal and an experimental comparison is conducted on the various implementations on real scale applications in the context of GIS.

Partially Ordered preferences applied to the site location problem in urban planning

This paper presents an application that aims at identifying optimal locations based on partially ordered constraints. It combines a tool developed in this project that allows the management of partially ordered constraints and a Geographical Information System (GIS) allowing spatial data mapping and analysis.

Belief change and pre-orders: a brief overview

This paper deals with iterated belief change. Epistemic states are suitable to represent an intelligent agents knowledge. Most of the time, when dealing with geographic information, the agent faces incomplete, uncertain, or inaccurate information and needs a mechanism for either revision, update, or fusion to handle their change in beliefs in the presence of new items of information. After some preliminaries on the representation of epistemic states by means of pre-orders, the paper presents three approaches to belief change: revision, update, and fusion. For each of these approaches, the background, postulates, representation by pre-orders, and semantic and syntactic requirements are given. In each case, the approaches are illustrated by examples.