Interval-based possibility theory: Conditioning and probability/possibility transformations • Amélie Levray
- Advisor :
- Salem Benferhat
- Co-Supervisor :
- Karim Tabia
- PhD defended on :
- faculté des sciences
This thesis contributes to the development of efficient formalisms to handle uncertain information. Existing formalisms such as probability theory or possibility theory are among the most known and used settings to represent such information. Extensions and generalizations (e.g. imprecise probability theory, interval-based possibility theory) have been provided to handle uncertainty such as incomplete and ill-known knowledge and reasoning with the knowledge of a group of experts. We are particularly interested in reasoning tasks within these theories such as conditioning.
The contributions of this thesis are divided in two parts. In the first part, we tackle conditioning in interval-based possibilistic framework and set-valued possibilistic framework. The purpose is to develop a conditioning machinery for interval-based possibilistic logic. Conditioning in a standard possibilistic setting differs whether we consider a qualitative or quantitative scale. Our works deal with both definitions of possibilistic conditioning. This leads us to investigate a new extension of possibilistic logic, defined as set-valued possibilistic logic, and its conditioning machinery in the qualitative possibilistic setting. These results, especially in terms of complexity, lead us to study transformations, more precisely from probability to possibility theories. The second part of our contributions deals with probability-possibility transformation procedures. Indeed, we analyze properties of reasoning tasks such as conditioning and marginalization. We also tackle transformations from imprecise probability theory to possibility theory with a particular interest in MAP inference.
- Gabriele Kern-Isberner - Professor at TU Dortmund University (Rapporteur)
- Gabriella Pasi - Professor at the University of Milano-Bicocca (Rapporteur)
- Hélène Fargier - Directeur de Recherche CNRS à l’IRIT - Université Paul Sabatier (Examinateur)
- Eric Lefevre - Professeur au LGI2A - Université d’Artois (Examinateur)
- Philippe Leray - Professeur au LS2N - Université de Nantes (Examinateur)
- Salem Benferhat - Professeur au CRIL - Université d’Artois (Directeur de thèse)
- Karim Tabia - Maître de conférences au CRIL - Université d’Artois (Encadrant)