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Core services of user modeling shell systems include the provision of representations for user model contents and for other relevant knowledge, and of reasoning mechanisms. These representation and reasoning facilities should be powerful and flexible, in order to satisfy both complex and specialized needs that developers of user modeling systems may have. This article first identifies these needs through a comprehensive overview of logic-based representation and reasoning in user modeling system. Then, the AsTRa (Assumption Type Representation) framework for logic-based user model representation and reasoning is presented. This framework obtains its power and flexibility through an integration of the two main scientific approaches that were pursued to date, namely the partition approach and the modal logic approach. The central notion of the framework is the `assumption type', a partition-like partial knowledge base for storing all assumptions about the user that are of the same type. Within assumption types, logic-based representation formalisms can be employed. The semantics of assumption types and content formalisms can be characterized in terms of modal logic, so that an extension to full modal logic is possible. Moreover, special mechanisms for handling so-called `negative assumptions' are developed, which are also firmly grounded in modal logic semantics. The paper concludes with a description of the user modeling shell BGP-MS as a prototypical implementation of AsTRa, and a discussion of the approach in the light of other user modeling shells.