Advanced Database Management System - Tutorials and Notes: Three valued logic

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## Three valued logic

It is a many-valued logic system. It is proposed to handle NULL values. For example, consider a condition ‘Age > 15’. This condition compares two values (one is stored in Age variable and the other is 15) and results in either TRUE or FALSE (Boolean logic). What if one of the operands is NULL? To handle such comparisons the three valued logic has been proposed. Three valued logic is sometimes called as Trivalent logic, Ternary logic or Trinary logic.

"SQL’s logic is an implementation of three valued logic".

Unlike Bivalent logic system (Boolean logic evaluates to TRUE or FALSE) there are three truth values such as TRUE, FALSE, and UNKNOWN in three valued logic system.

In three valued logic system, the logical operators are evaluated as follows;

• NOT x – evaluates to 1 – x
• x OR y – evaluates to max(x, y), ie., whichever is true then the result is true
• x AND y – evaluates to min(x,y), ie., one of them is false then the result is false.
You can observe the results from the following table;
 x y x AND y x OR y NOT x True True True True False True False False True True Unknown Unknown True False True False True True False False False False False Unknown False Unknown Unknown True Unknown True Unknown Unknown False False Unknown Unknown Unknown Unknown Unknown

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