Abstract
A query language is considered allowing queries which ask for the cardinality of a set of objects satisfying specified conditions, or ask whether or not some relations (equalities, inequalities, etc.) hold between the cardinalities of sets of objects satisfying some conditions. We describe a precise semantics of this language, and we give a complete axiom system for equivalent transformations of queries. By using these axioms we are able to transform any query into a normal form which makes the retrieval process more efficient.
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