Boolean Logic and Algebra

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

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:

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.