Entailment vs Implicature

Two kinds of meaning

Suppose someone tells you, "Some students passed the exam." You will almost certainly walk away believing two things: first, that at least one student passed; second, that not all of them did. Yet only the first belief is locked into the literal meaning. The second is a hint the speaker has dropped — and a hint they can take back without contradicting themselves.

That asymmetry is the core distinction in pragmatics between entailment and implicature. An entailment is a relation between sentences: A entails B if every situation that makes A true also makes B true. An implicature is a relation between a speaker and a hearer: by uttering A, the speaker conveys B, but B is not part of A's literal content.

Grice's 1967 William James lectures (published as part of Studies in the Way of Words, 1989) carved out implicature as a separate category of meaning precisely because the existing tools — truth tables, model-theoretic semantics — could not explain why "Some students passed" feels like a claim about not all when, strictly, it is not.

Entailment, formally

A sentence A entails a sentence B (written A ⊨ B) if and only if there is no possible situation in which A is true and B is false. Entailment is a one-way relation derived from the lexical and structural semantics of A. It does not depend on context, the speaker's intentions, or the hearer's beliefs.

Standard examples:

• "The cat sat on the mat" ⊨ "An animal sat on the mat" (because cat entails animal).
• "Marie murdered the duke" ⊨ "The duke is dead" (lexical entailment via murder).
• "All the windows are open" ⊨ "The kitchen window is open" (universal quantifier over a domain that includes the kitchen window).
• "John bought a Toyota" ⊨ "John bought a car" (hyponymy).

The classical test for entailment is contradiction on denial: A ⊨ B if and only if "A and not B" is contradictory. "Marie murdered the duke but the duke is alive" is contradictory, confirming the entailment.

Implicature, formally

Grice defines a conversational implicature as a piece of meaning that a hearer derives by assuming the speaker is being cooperative — observing the maxims of Quantity, Quality, Relation, and Manner — and asking what extra proposition would make the utterance cooperative in context.

The textbook example is the scalar implicature triggered by some. The English quantifiers form a Horn scale ⟨all, most, many, some⟩, ordered by informativeness. By the first quantity maxim ("Make your contribution as informative as required"), if a speaker had been in a position to say all, they would have. They said some. The hearer infers: not all. This inference is a Q-implicature — quantity-based — and it is calculated, not encoded.

Other classic implicatures:

• Quantity: "I ate three of the cookies" → I didn't eat four (scale of numerals).
• Relation ("Be relevant"): A: "I'm out of gas." B: "There's a station around the corner." → The station is open and sells gas.
• Manner ("Avoid prolixity"): "She turned the key and the engine started" → The engine started because she turned the key (temporal-causal ordering by reporting order).
• Quality flouting: "Tehran is in Turkey." (Said to a student giving wrong answers) → "You should know better."

Six properties that distinguish them

Property	Entailment	Conversational implicature
Defeasibility	None — guaranteed by truth conditions	Defeasible — can be overridden by context or cancellation
Cancellability	"…but in fact not" → contradiction	"…but in fact not" → coherent ("Some, in fact all, passed.")
Calculability	Falls out of compositional semantics; no reasoning required	Derived by Gricean reasoning over maxims and context
Conventionality	Tied to lexical / structural meaning of expressions	Not conventional — depends on what was not said
Detachability	Detachable — substitute synonyms and the entailment may differ if lexical content differs	Non-detachable — paraphrasing the same content carries the same implicature ("a few" carries the same Q-implicature as "some")
Reinforceability	Reinforcement is redundant ("She murdered him, and yes he is dead")	Reinforcement is natural ("Some, but not all, passed")

These six properties are the standard Gricean diagnostics. A meaning component is a conversational implicature if it satisfies all of them; an entailment satisfies none. (Conventional implicatures, presuppositions, and explicatures sit at intermediate points and are discussed below.)

A worked example: rain and picnics

Consider the conditional:

If it rains, the picnic is cancelled.

What does this commit the speaker to? Take three candidate inferences and run them through the diagnostics.

1. "If it rains, the picnic is cancelled" ⊨ "If it rains, the picnic does not happen." This is an entailment via the lexical meaning of cancelled. Denial yields contradiction: "*If it rains, the picnic is cancelled, but if it rains the picnic happens." Confirmed entailment.
2. "If it rains, the picnic is cancelled" suggests "If it doesn't rain, the picnic happens." This is the conditional perfection implicature — a Q-implicature on the scale of conditionals. We can cancel it: "If it rains, the picnic is cancelled. Of course, the picnic might also be cancelled for other reasons — wasps, illness, anything." No contradiction. Implicature, not entailment.
3. "If it rains, the picnic is cancelled" presupposes "There is a picnic planned." This survives negation — "If it rains, the picnic is not cancelled" still presupposes the planned picnic. This is a presupposition, a third category that we discuss below.

The same surface utterance carries three layers of meaning, each behaving differently under denial, negation, and cancellation. Pragmatics is the study of these layers.

Varieties of implicature

Not all implicatures are conversational. Grice distinguished:

• Generalized conversational implicatures (GCIs): arise by default in most contexts. Scalar implicatures (some → not all) and clausal implicatures (or → exclusive disjunction) are the canonical examples. Levinson's 2000 Presumptive Meanings argues these are so robust they should be modelled as defaults.
• Particularized conversational implicatures (PCIs): depend tightly on context. "I have a friend in the police" → "I can help you fix the parking ticket" only works in the right setup.
• Conventional implicatures: encoded by specific lexical items but not part of truth conditions. But conventionally implicates a contrast ("She is rich but unhappy"); even implicates unexpectedness; therefore implicates a causal link. These cannot be cancelled, yet they don't affect truth values either — a hybrid category that has spawned its own literature (Potts 2005, The Logic of Conventional Implicatures).

The presupposition contrast

Presupposition is the third major category, often confused with implicature. A presupposition is a backgrounded assumption that survives negation:

• "John stopped smoking" presupposes "John used to smoke."
• "John did not stop smoking" still presupposes "John used to smoke."

The standard test is the family of sentences: an inference is a presupposition if it survives negation, questioning, conditional embedding, and modal embedding. "Did John stop smoking?" / "If John stopped smoking, his lungs will recover." / "John might have stopped smoking." All carry the smoking presupposition.

Implicatures fail this test in important ways. The Q-implicature of some typically does not survive in negative contexts — "Not some, but all, passed" is fine and even informative — though in practice the projection patterns of scalar implicatures are subtle and have driven much research (Chierchia 2004; Sauerland 2004).

Cross-linguistic notes

Grice's framework was developed on English data, but the structural distinctions show up across languages, often with different lexical inventories driving different scalar inferences.

• Mandarin uses 一些 yīxiē ("some") with the same Q-implicature as English some; experimental work (Yang & Yang 2018) confirms native speakers reliably derive "not all".
• Japanese has a discourse particle も (mo, "even / also") that contributes a conventional implicature of additivity, parallel to English also but more grammaticalised.
• Russian aspectual pairs encode entailments that English achieves with implicature: the imperfective читал ("was reading") does not entail completion; the perfective прочитал entails it. English "I was reading the book" merely implicates non-completion, cancellable: "I was reading the book — and yes, I finished it."

The general lesson: the boundary between what a language entails and what it leaves to implicature is itself a typological variable.

Why the distinction matters

The entailment/implicature divide shows up in everyday domains:

• Legal interpretation: contracts and statutes are read for entailments, not implicatures. "Smoking is prohibited" entails lighting a cigarette is prohibited; it does not entail vaping is, even if speakers might implicate it.
• NLP: NLI benchmarks like SNLI and MultiNLI label pairs as entailment / contradiction / neutral, ignoring implicature; LLMs learn implicature distributionally and often confuse it with entailment.
• Politics and journalism: politicians exploit cancellability — say something that implicates X, then deny ever having entailed X.

Common pitfalls

• "It can't be cancelled, so it must be an entailment." Conventional implicatures cannot be cancelled either, but they are not entailments. Use the negation test to separate.
• "Implicatures are just connotations." No — implicatures are calculable propositions that satisfy specific Gricean tests. Connotations are vague affective associations; they don't pass calculability.
• "Pragmatics handles everything outside semantics." Most pragmatic theories now recognise explicatures (Sperber & Wilson 1986; Carston 2002) — pragmatically enriched truth-conditional content, falling between literal semantics and implicature.
• Conflating presupposition with implicature. Presuppositions survive negation; implicatures normally don't. The diagnostic is mechanical and decisive.
• Treating all "what is meant" as implicature. Many speaker-meanings are direct entailments of the literal sentence in context (resolution of indexicals, anaphora, ellipsis) rather than implicatures.