Abstract
Usual propositional possibilistic logic formulas are pairs made of a classical logic formula associated with a weight thought of as a lower bound of its necessity measure. In standard possibilistic logic, only conjunctions of such weighted formulas are allowed (a weighted classical conjunction is equivalent to the conjunction of its weighted conjuncts, due to the min-decomposability of necessity measures). However, the negation and the disjunction of possibilistic logic formulas make sense as well. They were briefly introduced by the authors some years ago, in a multiple agent logic context. The present paper hints at the multi-tiered logic that is thus generated, and discusses its semantics in terms of families of possibility distributions. Its practical interest for expressing higher order epistemic states is emphasized.
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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 (LNAI), vol. 5590, pp. 805–816. Springer, Heidelberg (2009)
Benferhat, S., Hué, J., Lagrue, S., Rossit, J.: Interval-based possibilistic logic. In: Proc. 22nd Inter. Joint Conf. on Artif. Intellig (IJCAI 2011), Barcelona (July 16-22, 2011)
Boldrin, L., Sossai, C.: Local possibilistic logic. Journal of Applied Non-Classical Logics 7(3), 309–333 (1997)
Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, D.M., et al. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, Oxford (1994)
Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems 144, 3–23 (2004)
Dubois, D., Prade, H.: Toward multiple-agent extensions of possibilistic logic. In: Proc. IEEE Inter. Conf. on Fuzzy Systems (FUZZ-IEEE 2007), London (UK), pp. 187–192 (July 23-26, 2007)
Dubois, D., Prade, H., Schockaert, S.: Rules and meta-rules in the framework of possibility theory and possibilistic logic. Scientia Iranica,18, Special issue dedicated to the 90th birthday of L. A. Zadeh (to appear, 2011)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)
Zadeh, L.A.: PRUF: A meaning representation language for natural languages. Int. J. of Man-Machine Studies 10, 395–460 (1978)
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Dubois, D., Prade, H. (2011). Generalized Possibilistic Logic. In: Benferhat, S., Grant, J. (eds) Scalable Uncertainty Management. SUM 2011. Lecture Notes in Computer Science(), vol 6929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23963-2_33
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DOI: https://doi.org/10.1007/978-3-642-23963-2_33
Publisher Name: Springer, Berlin, Heidelberg
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