People mean more than they say. Conversational implicature is the name for everything in between.

Conversational implicature is meaning a speaker communicates beyond the literal content of what is said, which the listener infers from context and from the assumption that the speaker is cooperative. Asked whether a restaurant is good, someone says the parking is easy, and the listener concludes the food is not. The implied meaning is the real answer.

If a polar question needed the word yes or no to get its answer, these replies would leave the asker guessing. A majority of five readers found a clear yes or no in 86 % of them.

The cooperative principle is Grice's general expectation that participants in a conversation contribute what is required, at the stage where it is required, for the purpose of the exchange. Listeners interpret utterances on that assumption. When an utterance seems to break it, the listener looks for a meaning that keeps it.

The maxims of conversation are Grice's four categories of expectation: quantity, quality, relation and manner. Say as much as needed and no more, say what you believe true, be relevant, and be clear. Implicatures arise when a speaker follows them, and when a speaker visibly breaks them.

Conventional implicature is meaning attached to particular words, independent of context, such as the contrast carried by but or the consequence carried by therefore. It cannot be cancelled without contradiction. Grice set it apart from conversational implicature.

Entailment is what follows necessarily from what is said: if all guests left, some guests left. An implicature can be cancelled and an entailment cannot. The distinction separates what a text commits to from what it suggests.

A particularised conversational implicature depends on a specific context. It is getting late, said at a party, means let us go home. In another situation the same words imply nothing of the kind.

If context cost nothing to read, both rows would show the same scores. Both readers lose accuracy once the meaning depends on the situation, and GPT-4 loses more.

A generalised conversational implicature arises in most contexts unless something blocks it. I ate some of the cake normally implies that I did not eat all of it. Stephen Levinson built a theory of default meanings on this class.

A scalar implicature is the inference from a weaker expression on a scale to the negation of a stronger one, such as from some to not all, or from warm to not hot. It is the most studied implicature. Queries and reviews are full of such scales.

Calculability is the property that an implicature can be worked out from what was said, the context and the cooperative principle. If a meaning cannot be derived this way, it is not a conversational implicature. It makes implied meaning explainable.

Cancellability is the property that an implicature can be withdrawn without contradiction, as in some of the guests came, in fact all of them did. It is the main test for implicature. Pages that correct an implied assumption use it deliberately.

Flouting is the open violation of a maxim to communicate something indirectly. A reference letter that praises only handwriting flouts quantity and implies that the candidate is weak. Irony and understatement flout quality.

The Q-principle, named for quantity, tells a speaker to say as much as they can and lets the listener infer that nothing stronger holds. Laurence Horn formulated it, and Stephen Levinson developed his own version. Scalar implicatures follow from it.

Paul Grice, a British philosopher, introduced conversational implicature, the cooperative principle and the maxims in his William James Lectures at Harvard in 1967, published as Logic and Conversation in 1975. He showed that meaning depends on recognised intentions. Pragmatics as a discipline grew from this.

Stephen Levinson, a linguist and anthropologist, developed a theory of generalised conversational implicatures as default inferences, set out in Presumptive Meanings in 2000. He formulated the Q-, I- and M-principles. His work makes defaults central to meaning.

Robyn Carston argued that generalised and particularised implicatures form a continuum, and that much of what Griceans call implicature belongs to explicit content. Her work connects Grice to relevance theory. It moved the border between said and meant.

The tests, the formal models and the misuse. The usual treatment explains Grice's principle, the maxims and scalar implicature. It leaves out the further tests that separate implicature from entailment, the principles of Horn and Levinson, the categories between said and implied, the computational and game-theoretic models, the evaluation of language models, and the use of implicature to mislead while telling the truth. For search, that missing part decides whether a system understands what a query means or only what it says.

Non-detachability is the property that an implicature stays when the same content is expressed in other words, except for manner implicatures. It shows that the implied meaning attaches to what is said, beyond the choice of words. Rephrasing a query often keeps its implied meaning.

Reinforceability is the property that an implicature can be stated explicitly without sounding redundant, as in some, but not all, of the guests came. Jerrold Sadock proposed it as a test. It separates implicature from entailment, which sounds repetitive when stated.

The R-principle, from Laurence Horn, tells a speaker to say no more than necessary and lets the listener infer a richer, stereotypical meaning. It works against the Q-principle. Together they explain why some sentences are understood as more and others as less than they say.

Horn's division of pragmatic labour holds that unmarked, simple expressions get stereotypical interpretations and marked, longer expressions get unusual ones. He stopped the car means normally, and he caused the car to stop suggests something odd. The form of a query signals which reading is meant.

An explicature is the explicit content of an utterance, developed by context into a full proposition, a concept from relevance theory. Some meanings that Grice would call implicatures count as explicit on this view. The boundary decides what a sentence is taken to state.

An impliciture, a term by Kent Bach, is content that is implicit in what is said without being a separate implicature, as in you are not going to die said to a child with a small cut, meaning from this cut. It lies between the explicit and the implied. Short queries are full of implicitures.

Opting out is the open refusal to cooperate, as in I cannot say more. It suspends the maxims without violating them secretly. It is different from misleading, and the difference matters in law and in answers.

A maxim clash occurs when a speaker cannot satisfy one maxim without breaking another, for example saying as much as needed without saying something unproven. The listener infers the reason for the compromise. Somewhere in the south of France implies that the speaker does not know more.

An embedded implicature is an implicature that seems to arise inside a clause, under an operator such as if or or, beyond the level of the whole sentence. Its existence is debated between pragmatic and grammatical theories. It matters for queries with conditions and alternatives.

An intrusive implicature is implied content that affects the truth conditions of a larger sentence. Taking the medicine and getting better is not the same as getting better and taking the medicine. The order implies a cause, and the cause changes what is claimed.

The I-principle, one of Levinson's three, tells the listener to enrich a minimal expression to its most specific, stereotypical interpretation. A secretary implies a typical secretary unless something marks otherwise. It explains strengthened default readings.

The M-principle, Levinson's manner principle, holds that a marked expression signals a non-stereotypical situation. Choosing an unusual form implies an unusual meaning. It formalises Horn's division of pragmatic labour.

Relevance theory explains implicatures through the presumption of optimal relevance: the listener follows the path of least effort until the utterance yields enough effect. It replaces the maxims with one principle. It treats implicature as a matter of cognition.

Communicative intention is the speaker's intention that the listener recognise what they intend to convey. Grice made recognition of intention the core of meaning. Implicature depends on the listener attributing an intention to the speaker.

The rational speech act model, developed by Michael Frank and Noah Goodman, describes listeners and speakers as reasoning about each other probabilistically. Implicatures emerge as the most likely intended meanings. It gives Gricean reasoning quantitative predictions.

A signalling game is a game-theoretic model in which a sender sends a signal and a receiver acts on it, going back to David Lewis's Convention from 1969. Implicatures appear as equilibria of strategic communication. It explains why shared meanings stabilise.

The epistemic step is the move from the speaker did not say all to the speaker knows that not all, which requires assuming the speaker is informed. Uli Sauerland described the difference between weak and strong implicatures in these terms. Without the step, only ignorance is implied.

An exhaustification operator is a silent grammatical element proposed to derive scalar implicatures inside the grammar, associated with Gennaro Chierchia, Danny Fox and Benjamin Spector. It makes a sentence mean only what it says and nothing stronger. The debate is about where implicatures are computed.

Alternative sets are the sets of expressions a speaker could have used instead, against which an utterance is interpreted, formalised in Mats Rooth's focus semantics. Some implies not all because all was an available alternative. The alternatives define what the speaker chose to leave out.

Pragmatic tolerance is the finding that listeners, especially children, notice an underinformative statement but tolerate it when asked for a yes or no, as Napoleon Katsos and Dorothy Bishop showed. Knowing and rejecting are separate steps. A judgement of true is not a judgement of well put.

Developmental pragmatics studies how children acquire the ability to understand implied meaning. Children often accept literally true but underinformative statements that adults reject. Difficulties with implicature can be mistaken for difficulties with meaning.

Language models are evaluated on implicature with benchmarks that ask them to interpret indirect answers and implied meanings, compared against human judgements. Such evaluations show whether a model understands what is meant or only what is said. Semantic accuracy alone does not capture this.

If language models read implied meaning the way people do, every row would sit near 86 %. Three of the four models sit closer to a coin flip.

Perjury by implication concerns testimony that is literally true but misleading. In Bronston v. United States in 1973, the Supreme Court of the United States held that a literally true answer is not perjury even if it implies something false. The law draws a line exactly where implicature begins.

Deceptive implicature is misleading someone through a true statement that implies a falsehood, which Jörg Meibauer analysed as a form of lying. Asked whether a product has been recalled, a seller says it passed its last test. Marketing uses this form more often than outright falsehood.

Customers communicate through implicature, in queries, reviews and questions, and they read pages the same way. A page that answers only the literal query misses the implied request, and a page that implies more than it can support loses trust. Implied meaning decides both conversion and credibility.

Answer what the query implies as well as what it says, state openly what the page does not claim, and avoid implying what cannot be backed. Where the implied need is unclear, ask back. That is the idea of Supervised Search: the page clarifies the meaning with the reader.