In boolean logic

Boolean logic

Boolean algebra is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations of...

, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or

Logical disjunction

In logic and mathematics, a two-place logical connective or, is a logical disjunction, also known as inclusive disjunction or alternation, that results in true whenever one or more of its operands are true. E.g. in this context, "A or B" is true if A is true, or if B is true, or if both A and B are...

. That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both of p and q are false. In grammar

Grammar

In linguistics, grammar is the set of structural rules that govern the composition of clauses, phrases, and words in any given natural language. The term refers also to the study of such rules, and this field includes morphology, syntax, and phonology, often complemented by phonetics, semantics,...

, nor is a coordinating conjunction

Grammatical conjunction

In grammar, a conjunction is a part of speech that connects two words, sentences, phrases or clauses together. A discourse connective is a conjunction joining sentences. This definition may overlap with that of other parts of speech, so what constitutes a "conjunction" must be defined for each...

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The NOR operator is also known as Peirce's arrow -- Charles Sanders Peirce introduced the symbol ↓ for it, and demonstrated that combining uses of the logical NOR suffices for expressing any logical operation on two variables.