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Finding a suitable fragment of interest in a nonschematic XML document with a simple keyword search is a complex task. To deal with this problem, this paper proposes a theoretical framework with a focus on an algebraic query model having a novel query semantics. Based on this semantics, XML fragments that look meaningful to a keyword-based query are effectively retrieved by the operations defined in the model. In contrast to earlier work, our model supports filters for restricting the size of a query result, which otherwise may contain a large number of potentially irrelevant fragments. We introduce a class of filters having a special property that enables significant reduction in query processing cost. Many practically useful filters fall in this class and hence, the proposed model can be efficiently applied to real-world XML documents. Several other issues regarding algebraic manipulation of the operations defined in our query model are also formally discussed.