Introduction to Boolean Logic 

What Is Boolean Logic?

Boolean logic refers to the system of mathematical logic called Boolean algebra, named after the English mathematician George Boole. It is used to create logical rules or statements. These logical statements are used to analyze, select, and process data that enters the FI-SL application component.

In the FI-SL application component, you can use Boolean logic to:

The FI-SL application component first analyzes the data using logical statements and then determines whether the data should be used. If the logical statement is true, the data is used; if the statement is false, the data is not used.

Uses of Boolean Logic

Boolean logic is used in:

To use Boolean logic in these programs, you create logical statements that are then used as formulas in the FI-SL system. For more information, see the following section Boolean Logical Statements.

For more information on using Boolean logic in ledger selection, Report Writer, rollups, validations, and substitutions, see Using Boolean Statements in FI-SL.

Boolean Logical Statements

A Boolean logical statement is a logical proposition that is either true or false. The following are examples of true and false statements:

Logical statements can be linked using operators. An operator links logical statements and defines how the statements should be processed. A combined statement is two or more logical statements linked together.

Boolean logic uses the following operators:

When you use this operator, both statements must be true for the combined statement to be true.

1.

Los Angeles is a city in California AND (2 + 2 = 4) (TRUE)

2.

(2 + 2 = 4) AND (10 < 6) (FALSE)

3.

(10 < 6) AND (2 + 2 = 4) (FALSE)

4.

(2 + 3 = 4) AND (10 < 6) (FALSE)

When you use this operator, at least one of the statements must be true for the combined statement to be true.

1.

Los Angeles is a city in California OR (2 + 2 = 4) (TRUE)

2.

Los Angeles is a city in California OR (10 < 6) (TRUE)

3.

(10 < 6) OR Los Angeles is a city in California (TRUE)

4.

Los Angeles is a city in Texas OR (10 < 6) (FALSE)

When you use this operator, the statement that follows the NOT operator must be false for the statement to be true.

1.

NOT (2 + 2 = 4) (FALSE)

2.

NOT (10 < 6) (TRUE)

When you use this operator, at least one statement must be false for the combined statement to be true.

1.

(2 + 2 = 4) NAND Los Angeles is a city in California (FALSE)

2.

(2 + 2 = 4) NAND (10 < 6) (TRUE)

3.

(10 < 6) NAND (2 + 2 = 4) (TRUE)

4.

(2 + 3 = 4) NAND (10 < 6) (TRUE)

When you use this operator, both statements must be false for the combined statement to be true.

1.

(2 + 2 = 4) NOR Los Angeles is a city in California (FALSE)

2.

(2 + 2 = 4) NOR (1 = 2) (FALSE)

3.

(2 + 1 = 4) NOR (2 + 2 = 4) (FALSE)

4.

(2 + 1 = 4) NOR (10 < 6) (TRUE)

When you use this operator, the two statements depend on each other to determine the truth value of the statement ("IF A, THEN B"). However, if the second statement is true or the first statement is false, the combined truth value is true.

1.

(1 = 1) --> (2 + 4 = 6) (TRUE)

2.

(2 + 2 = 4) --> (10 < 6) (FALSE)

3.

(10 < 6) --> (2 + 2 = 4) (TRUE)

4.

(10 < 6) --> (2 + 3 = 4) (TRUE)

When you use this operator, both statements must be true or both statements must be false for the combined statement to be true.

1.

(1 = 1) <-> (2 + 2 = 4) (TRUE)

2.

(1 = 1) <-> (10 < 6) (FALSE)

3.

(10 < 6) <-> (1 = 1) (FALSE)

4.

(2 + 3 = 4) <-> (10 < 6) (TRUE)

For more information on Boolean statements, see Creating Boolean Statements for the FI-SL System.

Truth Tables

Because statements can be linked with other statements and because logical statements are sometimes unclear, Boolean logic uses truth tables to determine if a combined statement is true or false.

A truth table assigns values (TRUE or FALSE) to each statement in a combined statement. Once the system has assigned a truth value to an individual statement, the system determines a truth value for the combined statements, depending on the operator that is used to link the statements.

The following is an example of a truth table:

Statement A

Statement B

A [Operator] B

TRUE

TRUE

X

TRUE

FALSE

X

FALSE

TRUE

X

FALSE

FALSE

X

 

This truth table shows all possible TRUE and FALSE combinations for statement A and statement B. The combined statement truth value (x) is determined by the operator that is used in the truth table. You can find truth tables for all Boolean operators under Using Boolean Operators in Truth Tables.