Abstract
Bipolar possibility theory relies on the use of four set functions. On the one hand, a weak possibility and a strong necessity measure are increasing set functions, which are respectively max-decomposable with respect to union and min-decomposable with respect to intersection. On the other hand, strong possibility and weak necessity measures are two decreasing set functions, which are respectively min-decomposable with respect to union and max-decomposable with respect to intersection. In the first part of the paper we advocate the use of the last two functions for modeling a notion of graded desire. Moreover, we show that the combination of weak possibility and strong possibility allows us to model a notion of realistic desire, i.e., a desire that does not only account for satisfactoriness but also for its epistemic possibility. In the second part of the paper we show that possibility theory offers a semantic basis for developing a modal logic of beliefs and desires.
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References
Banerjee, M., Dubois, D.: A simple modal logic for reasoning about revealed beliefs. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 805–816. Springer, Heidelberg (2009)
Benferhat, S., Dubois, D., Kaci, S., Prade, H.: Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions. Information Fusion 7, 135–150 (2006)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001)
Boutilier, C.: Towards a logic for qualitative decision theory. In: Principles of Knowledge Representation and Reasoning: Proc. of the 5th Int. Conf. (KR 1994), pp. 75–86. AAAI Press (1994)
Casali, A., Godo, L., Sierra, C.: A graded BDI agent model to represent and reason about preferences. Artif. Intell. 175, 1468–1478 (2011)
Dastani, M., Lorini, E.: A logic of emotions: from appraisal to coping. In: Proc. of AAMAS 2012, pp. 1133–1140. ACM Press (2012)
Dubois, D., Hajek, P., Prade, H.: Knowledge-driven versus data-driven logics. J. of Logic, Language, and Information 9, 65–89 (2000)
Dubois, D., Prade, H.: Resolution principles in possibilistic logic. Int. J. Appr. Reas. 4, 1–21 (1990)
Dubois, D., Prade, H.: Epistemic entrenchment and possibilistic logic. Artificial Intelligence 50, 223–239 (1991)
Dubois, D., Prade, H.: Possibility theory: qualitative and quantitative aspects. In: Gabbay, D., Smets, P. (eds.) Quantified Representation of Uncertainty and Imprecision. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 1, pp. 169–226. Kluwer (1998)
Dubois, D., Prade, H.: From Blanchés hexagonal organization of concepts to formal concept analysis and possibility theory. Logica Universalis 6(1), 149–169 (2012)
Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems 144, 3–23 (2004)
Fariñas del Cerro, L.: Resolution modal logic. Logique et Analyse 110-111, 153–172 (1985)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press (1995)
Gratch, J., Marsella, S.: A domain independent framework for modeling emotion. Cognitive Systems Research 5(4), 269–306 (2004)
Goldszmidt, M., Pearl, J.: Qualitative probability for default reasoning, belief revision and causal modeling. Artificial Intelligence 84, 52–112 (1996)
Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell University Press (1962)
Hume, D.: A Treatise of Human Nature. In: Selby-Bigge, L.A., Nidditch, P.H. (eds.). Clarendon Press, Oxford (1978)
Lang, J., van der Torre, L., Weydert, E.: Hidden Uncertainty in the Logical Representation of Desires. In: Proc. of Int. Joint Conf. on Artificial Intelligence, pp. 685–690. Morgan Kaufmann (2003)
Lang, J., van der Torre, L., Weydert, E.: Utilitarian Desires. J. of Autonomous Agents and Multi-Agent Systems 5, 329–363 (2002)
Lorini, E.: A dynamic logic of knowledge, graded beliefs and graded goals and its application to emotion modelling. In: van Ditmarsch, H., Lang, J., Ju, S. (eds.) LORI 2011. LNCS, vol. 6953, pp. 165–178. Springer, Heidelberg (2011)
Lorini, E., Prade, H.: Strong possibility and weak necessity as a basis for a logic of desires. In: Godo, L., Prade, H. (eds.) Working Papers of the ECAI 2012 Workshop on Weighted Logics for Artificial Intelligence (WL4AI 2012), Montpellier, pp. 99–103 (August 28, 2012)
Meyer, J.J., van der Hoek, W.: Epistemic Logic for AI and Computer Science. Cambridge University Press (1995)
Ortony, A., Clore, G., Collins, A.: The Cognitive Structure of Emotions. Cambr. Univ. Pr. (1988)
Sahlqvist, H.: Completeness and correspondence in the first and second order semantics for modal logic. In: Proc. of 3rd Scandinavian Logic Symp., pp. 110–143. North-Holland (1975)
Shackle, G.L.S.: Decision, Order, and Time in Human Affairs. Cambridge Univ. Press (1961)
Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Causation in Decision, Belief Change and Statistics, pp. 105–134. Kluwer (1988)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets & Syst. 1, 3–28 (1978)
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Dubois, D., Lorini, E., Prade, H. (2013). Bipolar Possibility Theory as a Basis for a Logic of Desires and Beliefs. In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds) Scalable Uncertainty Management. SUM 2013. Lecture Notes in Computer Science(), vol 8078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40381-1_16
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DOI: https://doi.org/10.1007/978-3-642-40381-1_16
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