Concept

Propositional variable

Overview

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

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

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1. The content of a belief, when expressed in words, is the same thing (or very nearly the same thing) as what in logic is called a "proposition." A proposition is a series of words (or sometimes a single word) expressing the kind of thing that can be asserted or denied.

   Bertrand Russell, The Analysis of Mind

   States what Propositional variable is.

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2. An example of this is, when the simple propositions are connected by the particle _or_; as, Either A is B or C is D; or by the particle _if_; as, A is B if C is D. In the former case, the proposition is called _disjunctive_, in the latter, _conditional_: the name _hypothetical_ was originally common to both. As has been well remarked by Archbishop Whately and others, the disjunctive form is resolvable into the…

   John Stuart Mill, A System of Logic

   States what Propositional variable is.

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3. Thus, step by step, the whole cycle of current mathematical ideas is capable of logical definition. The process is detailed and laborious, and, like all science, knows nothing of a royal road of airy phrases. The essence of the process is, first, to construct the notion in terms of the forms of propositions, that is, in terms of the relevant propositional functions, and secondly, to prove the fundamental truths…

   Alfred North Whitehead, The organisation of thought, educational and scientific

   States what Propositional variable is.

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Related ideas

• Negation
• Logical conjunction
• Logical connective
• Propositional logic
• Mathematical logic
• Domain of discourse
• Singular term
• Predicate (logic)
• Atomic formula
• Higher-order logic
• Truth function
• Latin script

Opposing perspectives

• First-order logic

Place in the tradition

Part of First-order logic.

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