nimplique

Nimplique is a term used in contemporary logic and philosophy to denote the relation "does not imply" between two propositions. It is typically discussed as a way to articulate the failure of implication in cases where one proposition being true does not guarantee the truth of another. The term is not part of the standard repertoire of mainstream logic but has appeared in scholarly papers, argumentation analyses, and online discussions as a concise way to express counterexamples to implication.

Etymology and scope are varied. Nimplique is a neologism likely formed from elements of the French expression n’impliquer pas or from English non-implication, and its exact usage differs among authors. In many treatments it is treated as a binary relation on propositions, distinct from the standard material implication connective.

Semantics typically treat A nimplique B as true precisely when A is true and B is false under the same valuation; equivalently, the conjunction A ∧ ¬B is satisfiable. Thus nimplique signals the possibility of a counterexample to the claim that A entails B.

Example: Let A be "the signal is green" and B be "the car will proceed through the intersection." Depending on traffic rules or external constraints, it is possible for A to hold while B does not, yielding A nimplique B in that valuation.

Usage and reception are varied because there is no universally adopted formal definition. Nimplique is most often used as a linguistic or analytic tool to discuss entailment, explanatory power, and the limits of inference, rather than as a standard logical connective.

See also: implication, non-implication, entailment, counterfactuals, non-monotonic reasoning.