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DATALOG can be used to specify a variety of class analyses for object-oriented programs as variations of a common framework. In this framework, the result of analysing a class is a set of DATALOG clauses whose least fixpoint is the information analysed for. Modular class analysis of program fragments is then expressed as the resolution of open DATALOG programs. We provide a theory for the partial resolution of sets of open clauses and define a number of operators for reducing such open clauses.