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The problem of deciding whether for a given Datalog program there is an equivalent nonrecursive program (corresponding to a positive relational algebra query, or, equivalently, a formula of positive existential first-order logic, or, as a special case, a conjunctive query) is known as the Datalog boundedness problem and is undecidable.
The CASE expression, for example, enables SQL to perform conditional branching within queries, providing a mechanism to return different values based on evaluated conditions. This logic can be particularly useful for data transformation during retrieval, especially in SELECT statements.
In SELECT statements SQL returns only results for which the WHERE clause returns a value of True; i.e., it excludes results with values of False and also excludes those whose value is Unknown. Along with True and False, the Unknown resulting from direct comparisons with Null thus brings a fragment of three-valued logic to SQL. The truth tables ...
The Boolean data type is primarily associated with conditional statements, which allow different actions by changing control flow depending on whether a programmer-specified Boolean condition evaluates to true or false. It is a special case of a more general logical data type—logic does not always need to be Boolean (see probabilistic logic).
In most logical systems, one proves a statement of the form "P iff Q" by proving either "if P, then Q" and "if Q, then P", or "if P, then Q" and "if not-P, then not-Q". Proving these pairs of statements sometimes leads to a more natural proof, since there are not obvious conditions in which one would infer a biconditional directly.
An equi-join is a specific type of comparator-based join, that uses only equality comparisons in the join-predicate. Using other comparison operators (such as <) disqualifies a join as an equi-join. The query shown above has already provided an example of an equi-join:
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In SQL's three-valued logic the law of the excluded middle, p OR NOT p, no longer evaluates to true for all p. More precisely, in SQL's three-valued logic p OR NOT p is unknown precisely when p is unknown and true otherwise. Because direct comparisons with Null result in the unknown logical value, the following query