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Jeffrey’s rule of conditioning in a possibilistic framework. (English) Zbl 1235.68232
Summary: Conditioning, belief update and revision are important tasks for designing intelligent systems. Possibility theory is among the powerful uncertainty theories particularly suitable for representing and reasoning with uncertain and incomplete information. This paper addresses an important issue related to the possibilistic counterparts of Jeffrey’s rule of conditioning. More precisely, it addresses the existence and uniqueness of the solutions computed using the possibilistic counterparts of the so-called kinematics properties underlying Jeffrey’s rule of conditioning. We first point out that, like in the probabilistic framework, in the quantitative possibilistic setting there exists a unique solution for revising a possibility distribution given the uncertainty bearing on a set of exhaustive and mutually exclusive events. However, in the qualitative possibilistic framework, the situation is different. In particular, the application of Jeffrey’s rule of conditioning does not guarantee the existence of a solution. We provide precise conditions where the uniqueness of the revised possibility distribution exists.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
03B42 Logics of knowledge and belief (including belief change)
68T27 Logic in artificial intelligence
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