negatable

Negatable is an adjective used in philosophy of language, linguistics, and logic to describe a statement, proposition, or predicate that can be negated in a meaningful, truth-conditional way. In formal logic, negation is an operator that forms the opposite of a given proposition; for any well-formed proposition P, the sentence "not P" is the negation of P. Thus, in that sense, most propositions are negatable, though the linguistic realization of negation can be more complex in natural language.

In natural language, negation interacts with syntax, semantics, and context. A sentence is typically considered negatable if a grammatically well-formed negation exists and both the original and negated forms are truth-conditionally informative. Questions, imperatives, and some speech acts fall outside the standard truth-conditional sense of negation, while others involve presupposition or implicature that affect how the negation is interpreted.

Examples illustrate the concept. "The cat is on the mat" is negatable: "The cat is not on the mat." "All students passed" is negatable, though its ordinary negation can be phrased as "Not all students passed" or as "There exists a student who did not pass," depending on desired emphasis and scope. Some sentences with presuppositions complicate negation, such as "The king stopped drinking," which presupposes that the king drank previously; its negation does not simply cancel that presupposition.

In logic and computer science, negation is a fundamental operation used to define complementary truth values or to express opposite conditions. The term negatable highlights the capacity of a statement to support a direct negation within the applicable formal or linguistic framework.