Traditionally, there have been two approaches to powerful logic-based user modeling: First, in the modal logic approach, there is one knowledge base that consists of formulas of one (modal) logic formalism. Second, the partition approach divides the user model into partial knowledge bases, mainly to distinguish between different types of assumptions about the user. For the user modeling shell system BGP-MS an approach to integrate partitions with modal logic was developed and later refined to become the user model representation and reasoning framework As-TRa, which is also applicable in the more general case of agent modeling. In this framework, however, there is a representational gap between partitions and modal logic. A specific kind of user model contents, which we call negative assumptions, falls into this gap. Since negative assumptions have been quite frequently used with BGP-MS, we developed specialized mechanisms for dealing with them. This paper gives a brief overview of AsTRa, and formally presents the above-mentioned mechanisms. Like the whole AsTRa framework, they are semantically related to modal logic, which is proven.
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