<logic> (Commonly known as "Boolean algebra") A mathematical system concerning the two truth values, TRUE and FALSE and the functions AND, OR, NOT. Two-valued logic is one of the cornerstones of logic and is also fundamental in the design of digital electronics and programming languages. The term "Boolean" is used here with its common meaning - two-valued, though strictly Boolean algebra is more general than this. Boolean functions are usually represented by truth tables where "0" represents "false" and "1" represents "true". E.g.: A | B | A AND B --+---+-------- 0 | 0 | 0 0 | 1 | 0 1 | 0 | 0 1 | 1 | 1 This can be given more compactly using "x" to mean "don't care" (either true or false): A | B | A AND B --+---+-------- 0 | x | 0 x | 0 | 0 1 | 1 | 1 Similarly: A | NOT A A | B | A OR B --+------ --+---+-------- 0 | 1 0 | 0 | 0 1 | 0 x | 1 | 1 1 | x | 1 Other functions such as XOR, NAND, NOR or functions of more than two inputs can be constructed using combinations of AND, OR, and NOT. AND and OR can be constructed from each other using DeMorgan's Theorem: A OR B = NOT ((NOT A) AND (NOT B)) A AND B = NOT ((NOT A) OR (NOT B)) In fact any Boolean function can be constructed using just NOR or just NAND using the identities: NOT A = A NOR A A OR B = NOT (A NOR B) and DeMorgan's Theorem. (2003-06-18)

Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.

In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value. This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for true and false.

In logic, the semantic principle (or law) of bivalence states that every declarative sentence expressing a proposition (of a theory under inspection) has exactly one truth value, either true or false. A logic satisfying this principle is called a two-valued logic or bivalent logic.

In logic, an infinite-valued logic (or real-valued logic or infinitely-many-valued logic) is a many-valued logic in which truth values comprise a continuous range. Traditionally, in Aristotle's logic, logic other than bivalent logic was abnormal, as the law of the excluded middle precluded more than two possible values (i.

In logic, a four-valued logic is any logic with four truth values. Several types of four-valued logic have been advanced.

Jaina seven-valued logic is system of argumentation developed by Jaina philosophers and thinkers in ancient India to support and substantiate their theory of pluralism. This argumentation system has seven distinct semantic predicates which may be thought of as seven different truth values.

In logic, a finite-valued logic (also finitely many-valued logic) is a propositional calculus in which truth values are discrete. Traditionally, in Aristotle's logic, the bivalent logic, also known as binary logic was the norm, as the law of the excluded middle precluded more than two possible values (i.

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory.