Where does entailment collide?

The relation of logical consequence: a set of statements entails another when there is no way for the first to be true and the second false, so the truth of the premises guarantees the truth of the conclusion. Logicians separate a semantic reading, written with the double turnstile, from provability in a formal system, written with the single turnstile, and Anderson and Belnap's 1975 Entailment: The Logic of Relevance and Necessity built a whole family of relevant logics to capture a stricter entailment in which the premises must actually bear on the conclusion. Here the referent is a formal guarantee between abstract statements, judged by truth in every case, not a probe of what ordinary sentences suggest, a labelled prediction task for a computer, or a rule about who may inherit land.[1]

Unit

A consequence relation between a premise set and a conclusion

Recovery means

Not applicable

Measured by

Established by proof in a formal calculus or by showing no interpretation makes the premises true and the conclusion false

A semantic relation between sentences, in which the truth of one sentence necessitates the truth of another as a matter of literal meaning: "the dog barked" entails "an animal made a sound," so you cannot assert the first and deny the second without contradiction. Chierchia and McConnell-Ginet's 2000 Meaning and Grammar used entailment as a core tool for pinning down what a sentence means, and carefully set it apart from presupposition, which survives negation, and from conversational implicature, which a speaker can cancel. The referent is a meaning relation between ordinary sentences, tested by native speakers' judgements of truth, and it differs from a formal proof relation, a benchmark a model is trained to score on, and a restriction on an estate.[2]

Unit

A one-way truth relation between two natural-language sentences

Recovery means

Not applicable

Measured by

Probed by native-speaker judgement, contradiction tests, and behaviour under negation to tell it apart from presupposition and implicature

The applied task, also called natural language inference, of deciding whether one piece of text can be inferred from another: given a premise and a hypothesis, a system labels the pair as entailment, contradiction, or neutral. Dagan, Glickman, and Magnini's 2006 The PASCAL Recognising Textual Entailment Challenge framed this as a benchmark, deliberately using a loose, human notion of "a person would say the hypothesis follows" rather than the strict guarantee logicians demand. The referent is a labelled prediction task with training data and accuracy scores, driven by what most readers would accept, and it is not the airtight relation of formal logic, the meaning relation studied by semanticists, or anything to do with inheritance law.[3]

Unit

A premise-hypothesis pair scored as entailment, contradiction, or neutral

Recovery means

Not applicable

Measured by

Operationalised as classification accuracy against human-annotated labels on benchmark corpora

In English land law, to entail an estate is to create a fee tail: a form of ownership that ties land to a fixed line of descent, so it passes only to the grantee's lineal heirs and cannot be freely sold or willed away. The device grew out of the 1285 statute De Donis Conditionalibus, and Simpson's 1986 A History of the Land Law traces how families used the entail to keep estates intact across generations and how courts and conveyancers later found ways to break it. The referent is a legal restriction on the inheritance of real property, defined by statute and deed, and it has nothing in common with a logical guarantee, a relation between sentence meanings, or a benchmark a computer is scored on.[4]

Unit

An estate settled on a fixed line of heirs by grant or statute

Recovery means

Not applicable

Measured by

Identified by the words of a deed or settlement and by the rules of law governing descent and how an entail may be barred