Symbolic Possibilistic Logic: Completeness and Inference Methods

Abstract : This paper studies the extension of possibilistic logic to the case when weights attached to formulas are symbolic and stand for variables that lie in a totally ordered scale, and only partial knowledge is available on the relative strength of these weights. A proof of the soundness and the completeness of this logic according to the relative certainty semantics in the sense of necessity measures is provided. Based on this result, two syntactic inference methods are presented. The first one calculates the necessity degree of a possibilistic formula using the notion of minimal inconsistent sub-base. A second method is proposed that takes inspiration from the concept of ATMS. Notions introduced in that area, such as nogoods and labels, are used to calculate the necessity degree of a possibilistic formula. A comparison of the two methods is provided, as well as a comparison with the original version of symbolic possibilistic logic.
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Claudette Cayrol, Didier Dubois, Fayçal Touazi. Symbolic Possibilistic Logic: Completeness and Inference Methods. 13th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2015), Jul 2015, Compiègne, France. pp. 485-495. ⟨hal-01334712⟩

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