An overview of possibilistic logic and its application to nonmonotonic reasoning and data fusion

International audienceThis paper provides a brief survey of possibilistic logic as a simple and efficient tool for handling nonmonotonic reasoning and data fusion. In nonmonotonic reasoning, Lehmann’s preferential System P is known to provide reasonable but very cautious conclusions, and in particular, preferential inference is blocked by the presence of “irrelevant” properties. When using Lehmann’s rational closure, the inference machinery, which is then more productive, may still remain too cautious. These two types of inference can be represented using a possibility theory-based semantics. The paper proposes several safe ways to overcome the cautiousness of these systems. One of these ways takes advantage of (contextual) independence assumptions of the form: the fact that δ is true (or is false) does not affect the validity of the rule “normally if α then β”. The modelling of such independence assumptions is discussed in the possibilistic framework. This paper presents a general approach for fusing several ordered belief bases provided by different sources according to various modes. More precisely, the paper provides the syntactic counterparts of different ways of aggregating possibility distributions, well-known at the semantic level