Boolean Logic and Algebra

 Logic is the basis of rationality and a foundation for mathematics, science and technology. Particularly for information technologies.     (Factasia)

Motivation: Philosophical Logic

• Sentences of conclusion over statements of truth
• A means for stating proofs in slightly more formal terms than "free-style" language
Sometimes referred to as "Propositional logic"

Motivation: A Formal Approach to Logic...

• A means of expressing the logical elements of algorithms
• In expressions
• In control statements
Motivation: a Mathematical Language ... an Algebra
• That can describe unambiguously everything we want the simplest hardware components to do, and
• That can be easily and directly implemented in real hardware.
Definitions

• A minimal Boolean algebra consists of the set of values {true, false} and three operations AND, OR, and NOT. It is an algebra over a binary domain.

• A Boolean value can be either true or false.

• A Boolean variable can be associated with a Boolean value representation:

The "truth values" are represented in many different ways:
• T, F
• 1, 0
• on, off
• non-zero, zero

Boolean variable identifiers must be disjoint from the set of identifiers of truth-values and the identifiers of the operators.

• A Boolean expression is built out of the constants true and false, variables, the three Boolean operations, and parentheses.

• We can use Truth tables to define the three Boolean operations, similar to the means that we used to describe arithmetic operations.

Biography: George Boole

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Last Updated 09/24/2000