Using Possibilistic Logic for Modeling Qualitative Decision: ATMS-based Algorithms

Article type: Research Article

Authors: Dubois, Didier | Berre, Daniel Le | Prade, Henri | Sabbadin, Régis

Affiliations: IRIT – Université Paul Sabatier – 31062 Toulouse Cedex (France). e-mail:{dubois, leberre, prade, sabbadin}@irit.fr

Note: [] Address for correspondence: IRIT - Universite Paul Sabatier - 31062 Toulouse Cedex (France)

Abstract: This paper describes a logical machinery for computing decisions, where the available knowledge on the state of the world is described by a possibilistic propositional logic base (i.e., a collection of logical statements associated with qualitative certainty levels), and where the preferences of the user are also described by another possibilistic logic base whose formula weights are interpreted in terms of priorities. Two attitudes are allowed for the decision maker: a pessimistic risk-averse one and an optimistic one. The computed decisions are in agreement with a qualitative counterpart to the classical theory of expected utility, recently developed by three of the authors. A link is established between this logical view of qualitative decision making and an ATMS-based computation procedure. Efficient algorithms for computing pessimistic and optimistic optimal decisions are finally given in this logical setting (using some previous work of the fourth author).

Keywords: qualitative decision, possibilistic logic, possibility theory, ATMS

DOI: 10.3233/FI-1999-371201

Journal: Fundamenta Informaticae, vol. 37, no. 1-2, pp. 1-30, 1999