Decision, nonmonotonic reasoning and possibilistic logic

The paper survey recent AI-oriented works in qualitative decision developed by the authors in the framework of possibility theory. Lottery-based and act-based axiomatics underlying pessimistic and optimistic criteria for decision under uncertainty are first briefly restated, when uncertainty and preferences are encoded with an ordinal scale. A logical machinery capable of computing optimal decisions in the sense of these criteria is presented. Then an approach to qualitative decision under uncertainty which does not require a commensurateness hypothesis between the uncertainty and the preference scales is proposed; this approach is closely related to nonmonotonic reasoning, but turns our to be ineffective for practical decision. Lastly, the modeling of preference as prioritized sets of goals, as sets of solutions reaching some given level of satisfaction, or in terms of possibilistic constraints is discussed briefly.

[1]  Peter Gärdenfors,et al.  Nonmonotonic Inference Based on Expectations , 1994, Artif. Intell..

[2]  Didier Dubois,et al.  Decision-theoretic foundations of qualitative possibility theory , 2001, Eur. J. Oper. Res..

[3]  Judea Pearl,et al.  From Conditional Oughts to Qualitative Decision Theory , 1993, UAI.

[4]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[5]  Craig Boutilier,et al.  Toward a Logic for Qualitative Decision Theory , 1994, KR.

[6]  Didier Dubois,et al.  Logical Representation and Computation of Optimal Decisions in a Qualitative Setting , 1998, AAAI/IAAI.

[7]  Didier Dubois,et al.  Possibility Theory as a Basis for Qualitative Decision Theory , 1995, IJCAI.

[8]  Didier Dubois,et al.  Epistemic Entrenchment and Possibilistic Logic , 1991, Artif. Intell..

[9]  Didier Dubois,et al.  Using Possibilistic Logic for Modeling Qualitative Decision: ATMS-based Algorithms , 1999, Fundam. Informaticae.

[10]  J. Neumann,et al.  Theory of Games and Economic Behavior. , 1945 .

[11]  Didier Dubois,et al.  New Semantics for Quantitative Possibility Theory , 2001, ECSQARU.

[12]  Judea Pearl,et al.  Qualitative Decision Theory , 1994, AAAI.

[13]  Abraham Wald,et al.  Statistical Decision Functions , 1951 .

[14]  Jon Doyle,et al.  Impediments to Universal Preference-Based Default Theories , 1989, KR.

[15]  Joseph Y. Halpern.  Defining Relative Likelihood in Partially-Ordered Structures , 1997, J. Artif. Intell. Res..

[16]  D. Dubois,et al.  Aggregation of decomposable measures with application to utility theory , 1996 .

[17]  Patrice Perny,et al.  Qualitative Models for Decision Under Uncertainty without the Commensurability Assumption , 1999, UAI.

[18]  Adriana Zapico,et al.  Axiomatic Foundations for Qualitative/Ordinal Decisions with Partial Preferences , 1999, IJCAI.

[19]  J. Kacprzyk,et al.  Aggregation and Fusion of Imperfect Information , 2001 .

[20]  Joseph Y. Halpern,et al.  Plausibility measures and default reasoning , 1996, JACM.

[21]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[22]  Luis Fariñas del Cerro,et al.  Qualitative Relevance and Independence: A Roadmap , 1997, IJCAI.

[23]  Didier Dubois,et al.  Nonmonotonic Reasoning, Conditional Objects and Possibility Theory , 1997, Artif. Intell..

[24]  Didier Dubois,et al.  Fuzzy constraints in job-shop scheduling , 1995, J. Intell. Manuf..

[25]  Rachid Alami,et al.  A Possibilistic Planner that Deals with Non-Determinism and Contingency , 1999, IJCAI.

[26]  Didier Dubois,et al.  Qualitative Decision Theory with Sugeno Integrals , 1998, UAI.

[27]  Judea Pearl,et al.  System Z: a Natural Ordering of Defaults with Tractable Applications to Nonmonotonic Reasoning^ , 1990 .

[28]  Jérôme Lang,et al.  Towards qualitative approaches to multi-stage decision making , 1998, Int. J. Approx. Reason..

[29]  Eric Raufaste,et al.  Empirical Evaluation of Possibility Theory in Human Radiological Diagnosis , 1998, ECAI.

[30]  Peter Gärdenfors,et al.  Knowledge in Flux , 1988 .

[31]  Jérôme Lang,et al.  Possibilistic logic as a logical framework for min-max discrete optimisation problems and prioritized constraints , 1991, FAIR.

[32]  Didier Dubois,et al.  Decision-Making under Ordinal Preferences and Comparative Uncertainty , 1997, UAI.

[33]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[34]  Dov M. Gabbay,et al.  Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning , 1994 .

[35]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[36]  Didier Dubois,et al.  From Semantic to Syntactic Approaches to Information Combination in Possibilistic Logic , 1998 .

[37]  Andrew P. Sage,et al.  Uncertainty in Artificial Intelligence , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[38]  H. Prade,et al.  Possibilistic logic , 1994 .

[39]  Didier Dubois,et al.  Possibility Theory: Qualitative and Quantitative Aspects , 1998 .

[40]  Didier Dubois,et al.  Conditional objects, possibility theory and default rules , 1996 .

[41]  Daniel Lehmann,et al.  What does a Conditional Knowledge Base Entail? , 1989, Artif. Intell..

[42]  Didier Dubois,et al.  Representing Default Rules in Possibilistic Logic , 1992, KR.

[43]  Blai Bonet,et al.  Arguing for Decisions: A Qualitative Model of Decision Making , 1996, UAI.

[44]  H. Moulin.  Axioms of Cooperative Decision Making , 1988 .