We present an approach to handle unavailable data sources during query execution over WWW which is based on partial evaluations. Syntax of the set-theoretic query language triangle open and some examples of queries are given. We define an ordinary and a lazy semantics for this language, Moreover, are introduce a universe of non-well-founded hereditarily finite protosets and an approximation relation on this universe in order to compare the partial answers to a query. A theorem about properties of the above semantics, in particular about correctness of lazy semantics is formulated.
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