Concept
Polish notation
Related concepts (20)
Arity
In logic, mathematics, and computer science, arity (ˈærᵻti) is the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank, but this word can have many other meanings. In logic and philosophy, arity may also be called adicity and degree. In linguistics, it is usually named valency. In general, functions or operators with a given arity follow the naming conventions of n-based numeral systems, such as binary and hexadecimal.
Exclusive or
Exclusive or or exclusive disjunction or exclusive alternation, also known as non-equivalence which is the negation of equivalence, is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator and by the infix operators XOR (ˌɛks_ˈɔ:r, ˌɛks_ˈɔ:, 'ksɔ:r or 'ksɔ:), EOR, EXOR, , , , ⩛, , and . It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true; the exclusive or operator excludes that case.
Infix notation
Infix notation is the notation commonly used in arithmetical and logical formulae and statements. It is characterized by the placement of operators between operands—"infixed operators"—such as the plus sign in 2 + 2. Binary relations are often denoted by an infix symbol such as set membership a ∈ A when the set A has a for an element. In geometry, perpendicular lines a and b are denoted and in projective geometry two points b and c are in perspective when while they are connected by a projectivity when Infix notation is more difficult to parse by computers than prefix notation (e.
Operand
In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. The following arithmetic expression shows an example of operators and operands: In the above example, '+' is the symbol for the operation called addition. The operand '3' is one of the inputs (quantities) followed by the addition operator, and the operand '6' is the other input necessary for the operation. The result of the operation is 9. (The number '9' is also called the sum of the augend 3 and the addend 6.
Operation (mathematics)
In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation. The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is a constant.
Negation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", standing for " is not true", written , or . It is interpreted intuitively as being true when is false, and false when is true. Negation is thus a unary logical connective. It may be applied as an operation on notions, propositions, truth values, or semantic values more generally. In classical logic, negation is normally identified with the truth function that takes truth to falsity (and vice versa).
Well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can be identified with the set of formulas in the language. A formula is a syntactic object that can be given a semantic meaning by means of an interpretation. Two key uses of formulas are in propositional logic and predicate logic.
Material conditional
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum. Material implication is used in all the basic systems of classical logic as well as some nonclassical logics.
Unary operation
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function f : A → A, where A is a set. The function f is a unary operation on A. Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial n!), functional notation (e.g. sin x or sin(x)), and superscripts (e.g. transpose A^T).
Universal quantification
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", or "for any". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable.