TUTORIAL SESSION

Plausible reasoning with incomplete information

Dr. Didier Dubois
UNIVERSITE PAUL SABATIER - IRIT - (Equipe ADRIA), France
dubois@irit.fr

Duration

3 hours

Abstract

We propose an introduction to methods for handling uncertainty due to incomplete information beyond probability theory. While probability theory seems to cover the whole range of representations of uncertainty, there are a certain number of reasons why a single probability distribution cannot qualify as a faithful representation of partial information. The latter is better handled by means of modalities dating back to the middle-age philosophy such as possibility and necessity that may account for the plausible and the certain, respectively.
Possibility theory is a simple uncertainty theory tailored for the handling of incomplete information and amenable to a purely qualitative treatment. The tutorial will provide basic notions of possibilistic logic, which is a non-monotonic ordered extension of propositional logic, and its use for a non-probabilistic rendering of exception-tolerant plausible reasoning. We shall also discuss the core issue of representing conditionals as three-valued formal models of if- then rules compatible with both possibility theory and probability theory, indicating the deep agreement between both approaches.

Possibilistic logic: a retrospective and prospective view

Non-Monotonic Reasoning and Uncertainty Theories

Tutorial Materials

Uncertainty
Probability vs. possibility
Possibility theory
Possibilistic logic
Conditioning without probability
Plausible non-monotonic reasoning : coping with exceptions
Relationship with probabilistic reasoning

Background Knowledge Expected of the Participants

Some notions of knowledge representation, propositional logic, probabilistic reasoning, logics for artificial intelligence

Qualifications of the Instructor(s)

Didier Dubois is a Research Advisor at IRIT, the Computer Science Department of Paul Sabatier University in Toulouse, France and belongs to the French National Centre for Scientific Resarch (CNRS). He holds a Doctorate in Engineering from ENSAE, Toulouse (1977), a Doctorat d'Etat from Grenoble University (1983) and an Honorary Doctorate from the Faculté Polytechnique de Mons, Belgium (1997). He is the co- author, with Henri Prade, of two books on fuzzy sets and possibility theory, and more than 15 edited volumes on uncertain reasoning and fuzzy sets. Also with Henri Prade, he coordinated the HANDBOOK of FUZZY SETS series published by Kluwer (7 volumes, 1998-2000, 2 of which he co-edited). It includes the book Fundamentals of Fuzzy Sets, edited again with H. Prade (Kluwer, Boston, 2000). More recently, he co-edited the tutorial handbook Decision-making Process - Concepts and Methods, ISTE London & Wiley, 2009. He has contributed about 200 technical journal papers on uncertainty theories and applications.
Since January 1, 1999, Didier Dubois has been co-Editor-in -Chief of
Fuzzy Sets and Systems. He is an Advisory Editor of the IEEE
Transactions on Fuzzy Systems. He is a member of the Editorial Board of several technical journals, such as the International Journal on Approximate Reasoning, General Systems, Journal of Applied Logic and Information Sciences among others. He is a former president of the International Fuzzy Systems Association (1995-1997). In 2002 he received the Pioneer Award of the IEEE Neural Network Society, and in
2012 the Scientific Excellence Award from the European Society For Fuzzy Logic And Technology (EUSFLAT).
His topics of interest range from Artificial Intelligence to Operations Research and Decision Sciences, with emphasis on the modelling, representation and processing of imprecise and uncertain information in reasoning, problem-solving tasks and risk analysis.

References

[1]	Dubois, D. Lang, J. and Prade, H. 1994. Possibilistic logic. In Gabbay, D.; Hogger, C.; and Robinson, J., eds., Handbook of logic in Artificial Intelligence and logic programming, volume 3. Clarendon Press - Oxford. 439–513.
[2]	S. Benferhat, D. Dubois and H. Prade, Nonmonotonic reasoning, conditional objects and possibility theory. Artificial Intelligence, 92 (1997), 259-276.
[3]	D.Dubois and H.Prade, Conditional objects as nonmonotonic consequence relationships.
[4]	Special issue on Conditional Event Algebra, IEEE Trans. on Systems, Man and Cybernetics, 24(12), 1724-1740, 1994.
[5]	Lehmann, D., and Magidor, M. 1992. What does a conditional knowledge base entail?
[6]	Artificial Intelligence 55:1– 60.
[7]	G. Kern-Isberner. Conditionals in Nonmonotonic Reasoning and Belief Revision - Considering Conditionals as Agents, volume 2087 of Lecture Notes in Computer Science. Springer, 2001.
[8]	ISBN 3-540-42367-2.
[9]	A. Gilio. Probabilistic reasoning under coherence in System P. Annals of Mathematics and Articial Intelligence, 34(1-3):5{34, 2002.
[10]	V. Biazzo, A. Gilio, T. Lukasiewicz, and G. Sanlippo. Probabilistic logic under coherence, modeltheoretic probabilistic logic, and default reasoning in System P. Journal of Applied Non-Classical Logics, 12(2):189{213, 2002.
[11]	Dubois D. Prade H. Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems. 2004. 144, 3-23 Didier Dubois, Henri Prade. Non-Monotonic Reasoning and Uncertainty Theories. In : Nonmonotonic Reasoning. Essays Celebrating its 30th Anniversary.. Gerhard Brewka, Victor Marek, Miroslaw Truszczynski (Eds.), College Publications, p. 141-176, Vol. 31, Studies in Logic, 2011.