Concept

Logical connective

Overview

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is an operator that combines or modifies one or more logical variables or formulas, similarly to how arithmetic connectives like

{\displaystyle +}

and

−

{\displaystyle -}

combine or negate arithmetic expressions. For instance, in the syntax of propositional logic, the binary connective

∨

{\displaystyle \lor }

(meaning "or") can be used to join the two logical formulas

{\displaystyle P}

and

{\displaystyle Q}

, producing the complex formula

∨

{\displaystyle P\lor Q}

Unlike in algebra, there are many symbols in use for each logical connective. The table "Logical connectives" shows examples.

Common connectives include negation, disjunction, conjunction, implication, and equivalence. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English "not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning.

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

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If our logic is to find the common world intelligible, it must not be hostile, but must be inspired by a genuine acceptance such as is not usually to be found among metaphysicians. Traditional logic, since it holds that all propositions have the subject-predicate form, is unable to admit the reality of relations: all relations, it maintains, must be reduced to properties of the apparently related terms. There are…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
States what Logical connective is; the author is tied to Logical connective in the knowledge graph.
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Economic causes operate through men's desire for possessions, and would be supreme if this desire were supreme, even if desire could not, from a philosophic point of view, be explained in materialistic terms. There is, therefore, no logical connection either way between philosophic materialism and what is called the "materialistic conception of history." It is of some moment to realize such facts as this, because…
Bertrand Russell, The Practice and Theory of Bolshevism
States what Logical connective is; the author is tied to Logical connective in the knowledge graph.
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This pattern of relationships among general abstract conditions is imposed alike on external reality, and on our abstract representations of it, by the general necessity that every thing must be just its own individual self, with its own individual way of differing from everything else. This is nothing else than the necessity of abstract logic, which is the presupposition involved in the very fact of interrelated…
Alfred North Whitehead, Science and the modern world
States what Logical connective is.
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Logical connective

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