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Possibilistic Logic: Complexity and Algorithms

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Handbook of Defeasible Reasoning and Uncertainty Management Systems

Part of the book series: Handbook of Defeasible Reasoning and Uncertainty Management Systems ((HAND,volume 5))

Abstract

Possibilistic logic is a logic of uncertainty tailored for reasoning under incomplete and partially inconsistent knowledge. At the syntactical level it handles formulae of propositional or first-order classical logic, to which are attached lower bounds of so-called degrees of necessity and possibility. The degree of necessity (resp. possibility) of a formula expresses to what extent the formula is entailed by (resp. compatible with) the available evidence. At the mathematical level, degrees of possibility and necessity are closely related to fuzzy sets [Zadeh, 1965; Zadeh, 1978] and possibilistic logic is especially adapted to automated reasoning when the available information is pervaded with vagueness. A vague piece of evidence can be viewed as defining an implicit ordering on the possible worlds it refers to, this ordering being encoded by means of fuzzy set membership functions. Hence, possibilistic logic is a tool for reasoning under uncertainty based on the idea of (complete) ordering rather than counting, unlike probabilistic logic. For a complete exposition of possibilistic logic see [Dubois et al., 1994]; a more general introduction to possibility theory and is in [Dubois and Prade, 1988].

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Authors and Affiliations

  1. IRIT, Université Paul Sabatier, Toulouse, France

    Jérôme Lang

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  1. Jérôme Lang
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Editors and Affiliations

  1. University of Fribourg, Switzerland

    Jürg Kohlas

  2. Universidad de Granada, Spain

    Serafín Moral

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Lang, J. (2000). Possibilistic Logic: Complexity and Algorithms. In: Kohlas, J., Moral, S. (eds) Handbook of Defeasible Reasoning and Uncertainty Management Systems. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1737-3_5

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  • DOI: https://doi.org/10.1007/978-94-017-1737-3_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5603-0

  • Online ISBN: 978-94-017-1737-3

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