A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs

In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should behave so as to maximize "qualitative expected utility." Our axiomatization of the qualitative utility is similar to the axiomatization developed by von Neumann and Morgenstern for probabilistic lotteries. We compare our results with other recent results in qualitative decision making.

[1]  Prakash P. Shenoy,et al.  On Spohn's rule for revision of beliefs , 1991, Int. J. Approx. Reason..

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

[3]  Moisés Goldszmidt,et al.  Rank-based Systems: A Simple Approach to Belief Revision, Belief Update, and Reasoning about Evidence and Actions , 1992, KR.

[4]  Wolfgang Spohn,et al.  Ordinal Conditional Functions: A Dynamic Theory of Epistemic States , 1988 .

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

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

[7]  A. Hasman,et al.  Probabilistic reasoning in intelligent systems: Networks of plausible inference , 1991 .

[8]  Ronen I. Brafman,et al.  On the Foundations of Qualitative Decision Theory , 1996, AAAI/IAAI, Vol. 2.

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

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

[11]  Nic Wilson,et al.  An Order of Magnitude Calculus , 1995, UAI.

[12]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[13]  Wolfgang Spohn,et al.  A general non-probabilistic theory of inductive reasoning , 2013, UAI.

[14]  Ronen I. Brafman,et al.  On the Axiomatization of Qualitative Decision Criteria , 1997, AAAI/IAAI.

[15]  Prakash P. Shenoy,et al.  Axioms for probability and belief-function proagation , 1990, UAI.

[16]  Judea Pearl,et al.  Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling , 1996, Artif. Intell..

[17]  E. W. Adams,et al.  The logic of conditionals , 1975 .

[18]  Prakash P. Shenoy,et al.  An Axiomatic Framework for Bayesian and Belief-function Propagation , 2013, UAI 1988.

[19]  Howard Raiffa,et al.  Games And Decisions , 1958 .

[20]  Moisés Goldszmidt,et al.  On the Relation between Kappa Calculus and Probabilistic Reasoning , 1994, UAI.

[21]  Henri Prade,et al.  On the Possibilistic Deceision Model: From Decesion under Uncertainty to Case-Based Decesion , 1999, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[22]  Daniel Hunter,et al.  Graphoids and natural conditional functions , 1991, Int. J. Approx. Reason..

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