Conflict-Based Belief Revision Operators in Possibilistic Logic
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In this paper, we investigate belief revision in possibilistic logic, which is a weighted logic proposed to deal with incomplete and uncertain information. Existing revision operators in possibilistic logic are restricted in the sense that the input information can only be a formula instead of a possibilistic knowledge base which is a set of weighted formulas. To break this restriction, we consider weighted prime implicants of a possibilistic knowledge base and use them to define novel revision operators in possibilistic logic. Intuitively, a weighted prime implicant of a possibilistic knowledge base is a logically weakest possibilistic term (i.e., a set of weighted literals) that can entail the knowledge base. We first show that the existing definition of a weighted prime implicant is problematic and need a modification. To define a revision operator using weighted prime implicants, we face two problems. The first problem is that we need to define the notion of a conflict set between two weighted prime implicants of two possibilistic knowledge bases to achieve minimal change. The second problem is that we need to define the disjunction of possibilistic terms. We solve these problems and define two conflict-based revision operators in possibilistic logic. We then adapt the well-known postulates for revision proposed by Katsuno and Mendelzon and show that our revision operators satisfy four of the basic adapted postulates and satisfy two others in some special cases.
Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence
Copyright 2012 AAAI Press. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the conference's website for access to the definitive, published version.
Artificial Intelligence and Image Processing not elsewhere classified