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In addition to basic equality and inequality conditions, SQL allows for more complex conditional logic through constructs such as CASE, COALESCE, and NULLIF.The CASE expression, for example, enables SQL to perform conditional branching within queries, providing a mechanism to return different values based on evaluated conditions.
As an example of why the restriction to domain independent first-order logic is important, consider .. (), which is not domain independent; see Codd's theorem. This formula cannot be implemented in the select-project-join fragment of relational algebra, and hence should not be considered a conjunctive query.
The atoms can be combined into formulas, as is usual in first-order logic, with the logical operators ∧ (and), ∨ (or) and ¬ (not), and we can use the existential quantifier (∃) and the universal quantifier (∀) to bind the variables. We define the set of formulas F[S,type] inductively with the following rules:
The relational algebra uses set union, set difference, and Cartesian product from set theory, and adds additional constraints to these operators to create new ones.. For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes.
An identifier may not be equal to a reserved keyword, unless it is a delimited identifier. Delimited identifiers means identifiers enclosed in double quotation marks. They can contain characters normally not supported in SQL identifiers, and they can be identical to a reserved word, e.g. a column named YEAR is specified as "YEAR".
See also: the {{}} template. The #if function selects one of two alternatives based on the truth value of a test string. {{#if: test string | value if true | value if false}} As explained above, a string is considered true if it contains at least one non-whitespace character.
A logical formula is considered to be in CNF if it is a conjunction of one or more disjunctions of one or more literals. As in disjunctive normal form (DNF), the only propositional operators in CNF are or ( ∨ {\displaystyle \vee } ), and ( ∧ {\displaystyle \wedge } ), and not ( ¬ {\displaystyle \neg } ).
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...