Propositional variable

Propositional variable

In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is a variable which can either be true or false. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher logics.

Formulas in logic are typically built up recursively from some propositional variables, some number of logical connectives, and some logical quantifiers. Propositional variables are the atomic formulas of propositional logic. For example, in a given propositional logic, we might define a formula as follows:

*Every propositional variable is a formula.
*Given a formula "X" the negation "¬X" is a formula.
*Given two formulas "X" and "Y", and a binary connective "b" (such as the logical conjunction ∧), then "(X b Y)" is a formula. (Note the parentheses.)

In this way, all of the formulas of propositional logic are built up from propositional variables as a basic unit.

ee also

* Boolean algebra (logic)
* Boolean datatype
* Boolean domain
* Boolean function
* Logical value
* Propositional logic


*Smullyan, Raymond M. "First-Order Logic". 1968. Dover edition, 1995. Chapter 1.1: Formulas of Propositional Logic.

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • propositional variable — noun A variable that can either be true or false …   Wiktionary

  • Propositional formula — In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional… …   Wikipedia

  • Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… …   Wikipedia

  • propositional function — n. Logic an expression containing at least one variable, that becomes a proposition when a constant is substituted for the variable (Ex.: x is a man) …   English World dictionary

  • propositional function — Logic. See sentential function. [1900 05] * * * Sentencelike expression that may be thought of as obtained from a sentence by substituting variables for constants occurring in the sentence. For example, x was a parent of y may be thought of as… …   Universalium

  • Propositional directed acyclic graph — A propositional directed acyclic graph (PDAG) is a data structure that is used to represent a Boolean function. A Boolean function can be represented as a rooted, directed acyclic graph of the following form: * Leaves are labeled with op (true),… …   Wikipedia

  • Variable proposicional — En lógica matemática, una variable proposional (también llamada variable sentencial o letra sentencial) es una variable que puede ser verdadera o falsa. Las variables proposicionales son los bloques de construcción básicos de las fórmulas… …   Wikipedia Español

  • Implicational propositional calculus — In mathematical logic, the implicational propositional calculus is a version of classical (two valued) propositional calculus which uses only one connective, called implication or conditional. In formulas, this binary operation is indicated by… …   Wikipedia

  • Predicate variable — In first order logic, a predicate variable is a predicate letter which can stand for a relation (between terms) but which has not been specifically assigned any particular relation (or meaning). In first order logic (FOL) they can be more… …   Wikipedia

  • formal logic — the branch of logic concerned exclusively with the principles of deductive reasoning and with the form rather than the content of propositions. [1855 60] * * * Introduction       the abstract study of propositions, statements, or assertively used …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.