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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 the theory of relational databases, a Boolean conjunctive query is a conjunctive query without distinguished predicates, i.e., a query in the form () (), where each is a relation symbol and each is a tuple of variables and constants; the number of elements in is equal to the arity of .
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 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 ...
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.
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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