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The semantics of SQL queries is formally defined by stating a set of rules that determine a syntax-driven translation of an SQL query to a formal model. The target model, called Extended Three Valued Predicate Calculus (E3VPC), is largely based on a set of well-known mathematical concepts. The rules which allow the transformation of a general E3VPC expression to a Canonical Form, which can be manipulated using traditional, two-valued predicate calculus are also given; in this way, problems like equivalence analysis of SQL queries are completely solved. Finally, the fact that reasoning about the equivalence of SQL queries using two-valued predicate calculus, without taking care of the real SQL semantics can lead to errors is shown, and the reasons for this are analyzed.

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