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 "freestyle" 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
 nonzero, zero
Boolean variable identifiers must be disjoint from the set of identifiers of truthvalues 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
Encyclopedia Entry
CS1104 Main Page
Last Updated 09/24/2000
© L.Heath, 2000, upgraded by J.A.N. Lee, 2000.