Binary logic is a set of rules for propositions that are either true or false, used in computer programming and mathematics. It includes operations like NOT, AND, and OR, and can be used to check for contradictions. Fuzzy logic allows for statements with degrees of truthfulness.
Binary logic, also called two-valued or Boolean logic, is a set of rules for dealing with propositions that must be true or false. Its main applications are in computer programming and mathematics, although there are also recreational games and puzzles based on more formal logic. The alternative to binary logic is “fuzzy” logic, which allows for statements that are neither true nor false and/or statements with degrees of truthfulness.
Propositions are the central operands of binary logic in the same way that numbers are the central operands of arithmetic. Generally denoted symbolically by a single letter, a proposition is a statement that must be either true or false, such as “Bill is over six feet tall” or “Two plus two equals five.” Subjective statements such as “Suzi is pretty” generally cannot be treated as propositions, since their truth depends on perspective. Clauses should also avoid pronouns, as a change in the pronoun’s referent changes the nature of the clause.
There are three operations common to all binary logic systems, AND, OR, and NOT. Also, many logic systems add IF operations. . . THEN, IF AND ONLY IF, and EOR. Notations vary widely, so it’s important to stay consistent in how you write binary logic.
The negation operation, NOT, is a unitary operation that applies to a single proposition. For a given proposition A, NOT-A is false if A is true and NOT-A is true if A is false. The AND operation creates a new statement composed of two simpler statements, such as “Bill is over six feet tall and two plus two equals five.” This new proposition is true if both of its component propositions are true; otherwise it is false. The OR operation also creates a new proposition from two simpler propositions, such as “Bill is over six feet tall, or two plus two equals five.” A OR B is true if A is true, B is true, or both are true. It is false only if both A and B are false.
Other operations are not included in all binary logic systems. The conditional operation, IF A THEN B, is false only when A is true and B is false and true otherwise, so it can also be expressed as NOT-A OR B. The IF AND ONLY IF operation, also called the biconditional operation, it is true if A and B are both true and false if A and B have different truth values. EOR operation is a strict alternative, A or B but not both. It is the opposite of the biconditional, true if A and B have different values and false if they have corresponding truth values.
The advantage of binary logic is that it provides a set of formal rules that can be used to check for contradictions in propositions. For this reason, logic has many applications in theoretical mathematics and computer science. The downside is that these rules only work with absolutely true or absolutely false statements and can give unreliable results when used with more vague statements.
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