Towards Decision Making via Expressive Probabilistic Ontologies

We propose a framework for automated multi-attribute decision making, employing the probabilistic non-monotonic description logics proposed by Lukasiewicz in 2008. Using this framework, we can model artificial agents in decision-making situation, wherein background knowledge, available alternatives and weighted attributes are represented via probabilistic ontologies. It turns out that extending traditional utility theory with such description logics, enables us to model decision-making problems where probabilistic ignorance and default reasoning plays an important role. We provide several decision functions using the notions of expected utility and probability intervals, and study their properties.

[1]  Thomas Lukasiewicz,et al.  Combining CP-Nets with the Power of Ontologies , 2013, AAAI.

[2]  Yann Chevaleyre,et al.  Expressive Power of Weighted Propositional Formulas for Cardinal Preference Modeling , 2006, KR.

[3]  John B. Kidd,et al.  Decisions with Multiple Objectives—Preferences and Value Tradeoffs , 1977 .

[4]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Thomas Lukasiewicz,et al.  Probabilistic Preference Logic Networks , 2014, ECAI.

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

[7]  Isaac Levi,et al.  The Enterprise Of Knowledge , 1980 .

[8]  R. M. Adelson,et al.  Utility Theory for Decision Making , 1971 .

[9]  Leon van der Torre,et al.  Reasoning with various kinds of preferences: logic, non-monotonicity, and algorithms , 2008, Ann. Oper. Res..

[10]  Nic Wilson,et al.  From Preference Logics to Preference Languages, and Back , 2010, KR.

[11]  Umberto Straccia.  Multi Criteria Decision Making in Fuzzy Description Logics: A First Step , 2009, KES.

[12]  Jérôme Lang,et al.  Logical representation of preferences for group decision making , 2000, KR.

[13]  J. Lygeros,et al.  Decision Making I , 2014 .

[14]  F. B. Vernadat,et al.  Decisions with Multiple Objectives: Preferences and Value Tradeoffs , 1994 .

[15]  Francesco M. Donini,et al.  Weighted Description Logics Preference Formulas for Multiattribute Negotiation , 2009, SUM.

[16]  Thomas Lukasiewicz,et al.  Expressive probabilistic description logics , 2008, Artif. Intell..

[17]  Francesco M. Donini,et al.  Computing Utility from Weighted Description Logic Preference Formulas , 2009, DALT.

[18]  Torsten Schaub,et al.  Expressing preferences in default logic , 2000, Artif. Intell..

[19]  Hans Tompits,et al.  A Classification and Survey of Preference Handling Approaches in Nonmonotonic Reasoning , 2004, Comput. Intell..

[20]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[21]  Yann Chevaleyre,et al.  Representing Utility Functions via Weighted Goals , 2009, Math. Log. Q..