Updating of a Possibilistic Knowledge Base by Crisp or Fuzzy Transition Rules

Boris Mailhé and Henri Prade

In this paper, partial knowledge about the possible transitions which can take place in a dynamical environment is represented by a set of pairs of propositional formulae, with the following intended meaning: If the first one is true then the second will be true at the next step. More generally, a certainty level representing the lower bound of a necessity measure can be associated with the second formula for modelling uncertain transitions. A possibilistic transition graph relating possible states can be deduced from these pairs and used for updating an uncertain knowledge base encoded in possibilistic logic and semantically associated to a possibility distribution. The updating of the base can be directly performed at the syntactic level from the transition pairs and the possibilistic logic formulas, in agreement with the semantics of the base and of the transitions. As there are many sets of pairs that represent the same transition graph, it is convenient to find a representative in this class that gives the easiest syntactic computations. Besides, a second type of weighted pairs of formulas is introduced for refining the representation of the available information about transitions. While the first type of pairs encodes the transitions that are not non-impossible (using necessity measures), the second type of pairs provides the transitions whose possibility is guaranteed. This constitutes a bipolar description of the possible transitions.

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