Core services of user modeling shell systems :include the provision of repr
esentations for user model contents and for other relevant knowledge, and o
f reasoning mechanisms. These representation and reasoning facilities shoul
d be powerful and flexible, in order to satisfy both complex and specialize
d needs that developers of user modeling; systems may have. This article fi
rst identifies these needs through a comprehensive overview of logic-based
representation and reasoning in user modeling system. Then, the AsTRa (Assu
mption Type Representation) framework for logic-based user model representa
tion and reasoning is presented. This framework obtains its power and flexi
bility through an integration of the two main scientific approaches that we
re pursued to date, namely the partition approach and the modal logic appro
ach. The central notion of the framework is the 'assumption type', a partit
ion-like partial knowledge base for storing all assumptions about the user
that are of the same type. Within assumption types, logic-based representat
ion formalisms can be employed. The semantics of assumption types and conte
nt formalisms can be characterized in terms of modal logic, so that an exte
nsion to full modal logic is possible. Moreover, special mechanisms for han
dling 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 shel
ls.