The general goal of information retrieval (IR) and information filtering (IF) is to dispatch relevant information objects to a user with respect to their specific information need. Such a process can be approximated by matching the representation K of a user's information needs with the description d of each incoming information object. Since users?s information needs will change over time, the matching process demonstrates nonmonotonicity in general. Moreover, as both K and d are only the partial descriptions of the underlying entities, uncertainty and inconsistency may arise during information matching. With a logic-based approach, the matching process can be characterised by K|~d, where |~ is a nonmonotonic inference relation. This paper examines how the non-trivial possibilistic deduction, a well-behaved nonmonotonic inference relation, can be applied to develop adaptive information filtering agents for alleviating information overload on the Web.