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What (who) is two-valued logic - definition

CLASSICAL LOGIC OF TWO VALUES, EITHER TRUE AND FALSE

Two-valued logic; Bivalent logic; Bivalence and related laws; Bivalence; Law of bivalence; Principle of Bivalence; Bivalence and realism; ThePrincipleOfBivalence; Suszko's thesis; Suszko thesis; Suszko reduction; Suszko's reduction; 2-valued logic; Two valued logic; Two value logic

two-valued logic

<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

PROPOSITIONAL CALCULUS IN WHICH THERE ARE MORE THAN TWO TRUTH VALUES

Multiple-valued logic; Many valued logic; Multivalued logic; Polyvalued logic; Many-valued logics; Belnap logic; Many-Valued Logics; Multi-valued logics; Multi-valued logic; Multiple valued logic; Multi valued logic; Poly-valued logic; Poly valued logic; Manyvalued logic; MV logic; M-V logic; MV-logic; Polyvalent logic; Applications of many-valued logic; Bochvar logic; History of many-valued logic; Rose logic

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.

https://en.wikipedia.org/wiki/Many-valued_logic

Three-valued logic

LOGIC SYSTEM IN WHICH THERE ARE THREE TRUTH VALUES INDICATING TRUE, FALSE AND SOME INDETERMINATE THIRD VALUE

Trivalent logic; Tribool; Trinary logic; Ternary logic; 3VL; 3-valued logic; Kleene logic; Law of excluded fourth; Triple-valued logic; Triple valued logic; Triple value logic; Triple-value logic; Three-valued logics; Non-boolean logic; Three valued logic; Three value logic; Trilean

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.

https://en.wikipedia.org/wiki/Three-valued_logic

Wikipedia

Principle of bivalence

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 formal logic, the principle of bivalence becomes a property that a semantics may or may not possess. It is not the same as the law of excluded middle, however, and a semantics may satisfy that law without being bivalent.

The principle of bivalence is studied in philosophical logic to address the question of which natural-language statements have a well-defined truth value. Sentences that predict events in the future, and sentences that seem open to interpretation, are particularly difficult for philosophers who hold that the principle of bivalence applies to all declarative natural-language statements. Many-valued logics formalize ideas that a realistic characterization of the notion of consequence requires the admissibility of premises that, owing to vagueness, temporal or quantum indeterminacy, or reference-failure, cannot be considered classically bivalent. Reference failures can also be addressed by free logics.

https://en.wikipedia.org/wiki/Principle of bivalence