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

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Sunday, 18 February 2018

Three valued logic

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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Three valued logic, the logic that evaluates to TRUE, FALSE, and UNKNOWN, How does SQL evaluates logic in its basic operations, SQL conditions and three valued logic, three valued logic, trivalent logic, ternary logic



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