entailment (n.)

A term derived from formal logic and now often used as part of the study of SEMANTICS; also called entailingness. It refers to a relation between a pair of PROPOSITIONS such that the truth of the second proposition necessarily follows from (is entailed by) the truth of the first, e.g. I can see a dog – I can see an animal. One cannot both assert the first and deny the second. In contemporary semantic discussion, entailment has come to be contrasted with PRESUPPOSITION, in particular because of their different behavior under NEGATION. Negating the entailing sentence causes the entailment relation to fail: thus She cannot see a dog does not entail She can see an animal: the latter may be true or false. However, both She has stopped buying books and She has not stopped buying books presuppose She has bought books. Directional entailingness is a feature of DETERMINERS, which may be described as either downward-entailing (in which the direction is from less specific to more specific) or upward-entailing (in which the direction is from more specific to less specific). For example, every is downward-entailing with respect to the NOUN PHRASE of which it is a part: from Every dog has four legs we may validly infer Every poodle has four legs (poodle is a HYPONYM of dog). By contrast, every is upward-entailing with respect to its VERB PHRASE: Every child likes a banana entails Every child likes a piece of fruit. The terms are especially used in the study of NEGATIVE POLARITY items.