Decision, Non-monotonicreasoning, possibilistic logic: An introductory survey of recent results

Salem Benferhat (1) , Didier Dubois (1, 2) , Hélène Fargier (1, 2) , Henri Prade (1, 2) , Régis Sabbadin (3)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique
3 UBIA - Unité de Biométrie et Intelligence Artificielle (ancêtre de MIAT)

The paper surveys 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 out 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.

Keywords: decision theory; nonmonotonic reasoning; possibility theory; preference; uncertainty

Domains: Artificial Intelligence [cs.AI]

Salem Benferhat, Didier Dubois, Hélène Fargier, Henri Prade, Régis Sabbadin. Decision, Non-monotonicreasoning, possibilistic logic: An introductory survey of recent results. Jack Minker. Logic-Based Artificial Intelligence, 597 (chapter 15), Springer, pp.333-358, 2001, The Springer International Series in Engineering and Computer Science book series (SECS), 978-1-4613-5618-9. ⟨10.1007/978-1-4615-1567-8_15⟩. ⟨hal-03300215⟩