Propositional variable, the Glossary

Table of Contents

1. 23 relations: Atomic formula, Boolean algebra, Boolean data type, Boolean domain, Boolean function, Domain of discourse, First-order logic, Free variables and bound variables, Higher-order logic, Latin script, Logical conjunction, Logical connective, Mathematical logic, Metavariable, Negation, Predicate variable, Propositional calculus, Propositional formula, Quantifier (logic), Singular term, Truth function, Truth value, Variable (mathematics).

2. Logic symbols
3. Propositional calculus

Atomic formula

In mathematical logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas.

See Propositional variable and Atomic formula

Boolean algebra

In mathematics and mathematical logic, Boolean algebra is a branch of algebra.

See Propositional variable and Boolean algebra

Boolean data type

In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted true and false) which is intended to represent the two truth values of logic and Boolean algebra.

See Propositional variable and Boolean data type

Boolean domain

In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true.

See Propositional variable and Boolean domain

Boolean function

In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually, or). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic.

See Propositional variable and Boolean function

Domain of discourse

In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.

See Propositional variable and Domain of discourse

First-order logic

First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

See Propositional variable and First-order logic

Free variables and bound variables

In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. Propositional variable and free variables and bound variables are logic symbols.

See Propositional variable and Free variables and bound variables

Higher-order logic

In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics.

See Propositional variable and Higher-order logic

Latin script

The Latin script, also known as the Roman script, is a writing system based on the letters of the classical Latin alphabet, derived from a form of the Greek alphabet which was in use in the ancient Greek city of Cumae in Magna Graecia.

See Propositional variable and Latin script

Logical conjunction

In logic, mathematics and linguistics, and (\wedge) is the truth-functional operator of conjunction or logical conjunction.

See Propositional variable and Logical conjunction

Logical connective

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Propositional variable and logical connective are logic symbols.

See Propositional variable and Logical connective

Mathematical logic

Mathematical logic is the study of formal logic within mathematics.

See Propositional variable and Mathematical logic

In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands for elements of some object language. Propositional variable and metavariable are logic symbols.

See Propositional variable and Metavariable

Negation

In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another proposition "not P", standing for "P is not true", written \neg P, \mathord P or \overline.

See Propositional variable and Negation

Predicate variable

In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not been specifically assigned any particular relation (or meaning). Propositional variable and predicate variable are logic symbols.

See Propositional variable and Predicate variable

Propositional calculus

The propositional calculus is a branch of logic.

See Propositional variable and Propositional calculus

Propositional formula

In propositional logic, a propositional formula is a type of syntactic formula which is well formed. Propositional variable and propositional formula are propositional calculus.

See Propositional variable and Propositional formula

Quantifier (logic)

In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula.

See Propositional variable and Quantifier (logic)

Singular term

A singular term is a paradigmatic referring device in a language. Propositional variable and singular term are Concepts in logic.

See Propositional variable and Singular term

Truth function

In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output.

See Propositional variable and Truth function

Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (true or false). Propositional variable and truth value are Concepts in logic.

See Propositional variable and Truth value

Variable (mathematics)

In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object.

See Propositional variable and Variable (mathematics)

See also

Logic symbols

• Ampersand
• Arrow (symbol)
• Conjunction/disjunction duality
• Descending wedge
• Double turnstile
• Existential quantification
• Free variables and bound variables
• Glossary of Principia Mathematica
• Horseshoe (symbol)
• List of logic symbols
• Literal (mathematical logic)
• Logical connective
• Logical connectives
• Logical constant
• Lozenge (shape)
• Metavariable
• Modal operator
• Non-logical symbol
• Predicate variable
• Propositional variable
• Sheffer stroke
• Symbol (formal)
• Tee (symbol)
• Therefore sign
• Tilde
• Triple bar
• Turned A
• Turnstile (symbol)
• Universal quantification
• Up tack
• Vertical bar
• Wedge (symbol)

Propositional calculus

• Clause (logic)
• Deductive closure
• DiVincenzo's criteria
• Formation rule
• Frege system
• Frege's propositional calculus
• Functional completeness
• Implicational propositional calculus
• Intermediate logic
• List of axiomatic systems in logic
• Literal (mathematical logic)
• Logical connectives
• Logical consequence
• Minimal axioms for Boolean algebra
• Negation introduction
• Negation normal form
• Nicod's axiom
• Predicate (mathematical logic)
• Predicate logic
• Principle of distributivity
• Proposition
• Propositional attitudes
• Propositional calculus
• Propositional formula
• Propositional proof system
• Propositional variable
• Propositions
• Resolution (logic)
• Rule of inference
• Rule of replacement
• Rules of inference
• Second-order propositional logic
• Stoic logic
• Substitution (logic)
• Suppes–Lemmon notation
• Tautology (logic)
• Truth table
• Unsatisfiable core
• Wholistic reference

References

[1] https://en.wikipedia.org/wiki/Propositional_variable

Also known as Proposition variable, Propositional symbol, Sentence letter, Sentential letter, Sentential variable.