Background on conversational implicature

  1. Background reading
  2. The Gricean maxims
    1. Additional maxims
    2. Variants
  3. Conversational implicature
    1. Definition
    2. Examples
    3. Non-examples
  4. Scalar implicature
  5. Looking ahead to indirect question–answer pairs
  6. Exercises

Background reading

I'm assuming for this course that you already have some experience with pragmatic theory (say, an introductory course or some time with a textbook). Thus, this section basically just assembles the raw ingredients for a theory of conversational implicature, so that we have them at hand for later discussions.

If you're completely new to pragmatics, I recommend reading Grice's classic 'Logic and conversation' as well as Wayne Davis's Stanford Encyclopedia's entry on implicature:

The readings I recommend specifically for this first unit:

The Gricean maxims

The Cooperative Principle
Make your contribution as is required, when it is required, by the conversation in which you are engaged.
Contribute only what you know to be true. Do not say false things. Do not say things for which you lack evidence.
Make your contribution as informative as is required. Do not say more than is required.
Relation (Relevance)
Make your contribution relevant.
Avoid obscurity.
Avoid ambiguity.
Be brief.
Be orderly.

Additional maxims

Davis 2010 states the following additional maxims, drawing on previous literature:

Be stylish, so be beautiful, distinctive, entertaining, and interesting.
Be polite, so be tactful, generous, praising, modest, agreeable, and sympathetic.


Lewis's (1976) version of quality emphasizes the uncertainty of our knowledge, allowing that we might be shy of conviction ("sufficiently close to 1") and yet still make assertions.

Lewisian quality Lewis 1976: 133
The truthful speaker wants not to assert falsehoods, wherefore he is willing to assert only what he takes to be very probably true. He deems it permissible to assert that A only if P(A) is sufficiently close to 1, where P is the probability function that represents his system of degrees of belief at the time. Assertability goes by subjective probability.

Joshi's (1982) view on quality demands that the speaker do some modeling of the hearer; this version of quality can be violated not just by unsupported or untruthful claims, but also by claims that generate misleading inferences.

Joshian quality (Joshi 1982, Hirschberg 1985, §2.3)
If S says that Q, then it must be that SB(Q) [S beliefs Q —CP]; further based on S's assessment of the mutual beliefs, it should not be possible for U, from what S has said (i.e. Q), to infer some other fact (say Q1) which S knows to be false. If there is such a possibility, then after saying Q, S should add further information to "square away" the mutual beliefs.

Horn (1984) reworks the Gricean maxims to remove some of their redundancy and to draw out the (productive) oppositions inherent in them. See also Blutner 1998, 2000 and van Rooy 2004 for formalizations of (some aspects of) Horn's framework.

Horn's Q and R Horn 1984, 1989, 1996
The Q Principle
Say as much as you can, modulo Quality and R.
The R Principle
Say no more than you must, modulo Q

Levinson's (2000) heuristics build on Horn's Q/R system but also place more emphasis on the importance of linguistic forms in driving pragmatic inferences.

Levinson's heuristics Levinson 2000
The Q Heuristic
What isn't said, isn't.
The I Heuristic
What is expressed simply is stereotypically exemplified.
The M Heuristic
What's said in an abnormal way isn't normal.

Asher and Lascarides (2008) is one of the few attempts I know of to confront the nature of pragmatic inference in situations in which the interlocutors have opposing goals. They seem not to be distributing this paper, but one can get a sense for the nature of their argument by reading Potts 2008, an unpublished commentary on their paper.

Conversational implicature


It's not uncommon for handbook articles and textbooks to avoid giving a definition at all, probably because Grice's original statement is problematically vague:

Conversational implicature Grice 1975
Proposition q is a conversational implicature of utterance U by agent A in context C just in case:
  1. it is mutual, public knowledge of all the discourse participants in C that A is obeying the Cooperative Principle;
  2. in order to maintain 1, it must be assumed that A believes q; and
  3. A believes that it is mutual, public knowledge of all the discourse participants that, to preserve 1, it must be assumed that A believes q

Hirschberg 1985: §2 identifies two really problematic aspects of this definition:

Hirschberg argues for the following definition; changes in Grice's original clauses are in bold, and the new clauses are (4)-(7). (I've made various modifications to Hirschberg's statement for the sake of readability; consult the original if you use with the definition in your own work.)

Conversational implicature (Hirschberg's version)
Proposition q is a conversational implicature of utterance U by agent A in context C just in case:
  1. A believes that it is mutual, public knowledge of all the discourse participants in C that A is obeying the Cooperative Principle (p. 19);
  2. A believes that, in order to maintain 1 given U, the hearer will assume that A believes q (p. 21)
  3. A believes that it is mutual, public knowledge of all the discourse participants that, to preserve 1, one must be assume that A believes q (p. 23)
  4. Cancelability: A potential implicature can be denied or suspended, directly or via background contextual assumptions or later clarifications. This is just to say that a calculation one might have performed can be blocked (p. 24).
  5. Nondetachability: For implicatures deriving from the information-theoretic maxims — quality, quantity, and relevance — forms do not matter, because the pressures govern only content. We therefore predict that synonymous forms generate all the same implicatures. Manner-based inferences create exceptions to this (p. 24).
  6. Nonconventionality: This is another perspective on calculability — the inferences should derive, not (solely) from lexical or constructional idiosyncrasies, but rather from pragmatic interactions (p. 24).
  7. Indeterminacy: "a conversational implicatum is often a disjunction of several possible interpretations of an utterance and is often indeterminate" (p. 24).

Cancelability, nondetachability, and nonconventionality are familiar from the literature and often discussed. Indeterminacy typically receives less treatment, though it is implicit in the property of reenforceability — a potential implicature can be directly stated with semantic content, thereby elevating it to an entailment, without a strong sense of redundancy. This is presumably because direct statement is a clear way of removing indeterminacy.

It's often said that conversational implicatures are universal. To the extent that the maxims reflect general features of rational information exchange, and to the extent that conversational implicatures are calculated directly from them, we expect universality. However, because contextual information (including deep cultural assumptions and views) are heavily involved in all implicature calculation, there is no expectation that people the world over will draw all the same implicatures in all the same situations — quite the contrary.

There is currently a lively debate about whether some (or all) implicatures are grammaticized, rather than calculated in the manner that Grice envisioned. Levinson (1995, 2000) argues that many conversational implicatures are default (presumptive) meanings, calculated by the hearer unless the speaker gives explicit counter-evidence. Chierchia (2004) takes a similar approach, arguing that scalar implicatures are calculated as part of the compositional semantics. Russell (2006) and Geurts (2009) seek to show that the embedded implicatures of Chierchia's paper can be derived by standard Gricean means. Chierchia, Fox, and Spector (2008) present what looks to my eye to be a kind of hybrid view, with lots of covert operators at LF but a broadly Gricean take of how those operators conspire to deliver implicatures. The journal Semantics & Pragmatics has published a series of papers and commmentaries on this issue, by Bart Geurts, Nausicaa Pouscoulous, Emmanuel Chemla, Robert van Rooij, Uli Sauerland, Michela Ippolito, Charles Clifton, and Chad Dube. I think those papers are a good place to go to get a sense for the nature of the debate at present.


    1. Kyle to Ellen: "I have $9."
    2. Implicature: Kyle does not $10.
    1. Contextual premise: Both Kyle and Ellen need $10 for their movie tickets.
    2. Contextual premise: It is mutual, public information that Kyle has complete knowledge of how much money he has on him
    3. Assume Kyle is cooperative at least insofar as he is obeying Quantity and Quality.
    4. Then he will assert what is maximally relevant, informative, and true.
    5. By (a), "I have $10" is more informative and relevant in this context than "I have $9".
    6. Therefore, Kyle must lack sufficient evidence to assert "I have $10".
    7. By contextual premise (b), he must lack evidence "I have $10" because it is false.

Comment: The implicature is heavily dependent upon the contextual assumptions. Two illustrations:

Comment: It presumably follows from the above that Kyle doesn't have $11, $12, etc. These are entailments of the implicature, but I think we cannot classify them as implicatures themselves, because they are not relevant in our context.

    1. A: Which city does Barbara live in?
    2. B: She lives in Russia.
    3. Implicature: B does not know which city Barbara lives in.
    1. Contextual premise: B is forthcoming about Barbara's personal life.
    2. Assume B is cooperative.
    3. Assume, towards a contradiction, that B does know which city Barbara lives in (the negation of the implicature).
    4. Supplying the city's name would do better on Relevance and Quantity than supplying just the country name.
    5. The contextual assumption is that B will supply such information.
    6. This contradicts the cooperativity assumption (b).
    7. We can therefore conclude that the implicature is true.

Comment: Here again the implicature is heavily dependent upon the contextual assumptions:

    1. A newspaper review of a newly opened play says that, in the third act, "Soap opera star Rachel Singer produced a series of sounds corresponding closely to the score of an aria from Rigoletto."
    2. Implicature: the reviewer believes that Rachel Singer's performance was not good.
    1. Assume the reviewer is cooperative.
    2. There is a shorter form, sang, competing with produced a series of sounds corresponding closely to the score of.
    3. By Levinson's M heuristic (what's said in an abnormal way isn't normal), the performance must have been unusual somehow.
    4. If it was unusually good, the reviewer would have said so directly, by cooperativity.
    5. If it was unusually bad, the reviewer would have said so directly, unless politeness was preventing him from doing so.
    6. Therefore, we conclude that the performance was unusually bad.

Comment: The implicature is highly dependent upon contextual assumptions, and it leans heavily on cooperativity:

Comment: I think we need to invoke Levinson's special purpose principles. I don't see a way to get this to follow from Manner as Grice originally gave it.


"Conversational implicature" is often used as a kind of general cover-term for all pragmatic enrichment. It seems very clear, though, that Grice had something more specific in mind. I believe Hirschberg's definition achieves something like the intended narrowing.

Here are two examples of pragmatic inference that, I argue, fall outside of the bounds of our full definition:

    1. B said that X conveys nothing about the speaker's commitment towards X, simply because it is possible to say both true and false things.
    2. However, such statements commonly interact with information in the common ground so as to lead speakers to conclude from such statements that X is in fact true. For example, if B is a trusted source for X-type information, we might infer X from such a claim.
    3. However, the inference that X is very unlikely to be a conversational implicature, because we can consistently maintain both that the author was cooperative and that he does not endorse it. (This might in fact be the pretense of a journalist who wrote such a sentence.)
    1. A: "Was the movie good?"
    2. B: "It was outstanding!"
    1. B's response conveys "Yes" as a response to the original question, though "Yes" is not encoded.
    2. However, this is an entailment rather than an implicature. The only role for the maxims in this calculation is at the level of quality.
    3. The meaning is not cancelable.

Scalar implicature

Scalar implicature
An utterance U conveys a scalar conversational implicature iff there are alternative utterances U' that are at least as relevant as U in the discourse and that are communicatively stronger than U. (The content of this implicature will depend on the context, the nature of the utterance competition, and other pragmatic factors.)

Example (1) and example (2) above are scalar implicatures. The cardinal determiners provide the scale in (1), and the conceptual hierarchy that includes Moscow, Russia provides the scale in (2).

It is often fruitful to think of the alternative utterances U' being generated by replacing the scalar term (or terms) with their contextually stronger alternatives. Gazdar (1979a,b) pursues this approach in his formalism. For relevant discussion, see Sauerland 2004, Fox and Katzir 2009.

I think it is still an open question whether we can truly reduce scalar implicature to competition at the lexical level. However, for computational work, it is certainly useful to think in these terms. It means that we can pre-compile the lexical (and perhaps constructional) scales, and it suggests that there might be syntactic methods for constructing the alternative utterances that enter into scalar implicature calculation. This won't obviate the need to reason in terms of the context, but it does provide us with useful pieces to work with.

One of the central findings of Hirschberg (1985: §4) is that the scales involves in scalar implicature are actually partial orderings. For example, while Moscow, Russia is a fragment of the scale needed for (2), we should flesh it out to {Moscow, Petersburg, ...}, Russia.

Logical scales, ordered by entailment, are just one of a wide variety of different relationships that are scalar in the relevant sense. We should speak instead of a general notion of pragmatic or contextual strength (Horn 1972, 1989, Hirschberg 1985).

The scalar ordering is not always the expected one. For example, in most contexts, the cardinal determiners will be ordered so that one (or maybe zero is the weakest element), but this can be reversed — for example, if the operator is in the scope of a negation or if the contextual goal favors smaller numbers (e.g., dieting). This helps make the point that contextual factors are central even to implicatures that seem to be lexical.

Hirschberg (1985: §4) discusses each of these points in greater detail. Please see the chapter for additional details. This will also help you with the coming experiments, since our corpus includes many (sometimes slightly modified) examples drawn from that chapter.

Looking ahead to indirect question–answer pairs

It would be too much to try to computationally explore conversational implicature in general. The phenomena are too diverse and complex. To help make the domain more manageable, we will focus on simple dialogues consisting of just a polar question and an indirect answer to that question. We'll turn next to a new annotated corpus of such data. For now, I'll illustrate the relevant phenomena with a famous real-life example, discussed at length by Solan and Tiersma 2005.

  1. Context: The defendant, Samuel Bronston, was president of Samuel Bronston Productions, Inc., a movie production company. He had personal as well as company bank accounts in various European countries. His company petitioned for bankruptcy. At the bankruptcy hearing, the following exchange occurred between the lawyer for the creditor and Bronston [who was under oath —CP]:
    1. Prosecutor: Do you have any bank accounts in Swiss banks, Mr. Bronston?
    2. Bronston: No, sir.
    3. Prosecutor: Have you ever?
    4. Bronston: The company had a bank account there for about six months, in Zurich.
    The truth: Bronston earlier had a large personal bank account in Switzerland for five years, where he had deposited and drawn checks totaling more than $180,000.

It's a testament to the automatic nature of pragmatic enrichment that no one in the courtroom insisted that Bronston give a direct answer to the question. One of the appealing things about small dialogues like this is that they seem to very reliably trigger pragmatic inferences in us; when confronted with a partial answer of this kind, we have a natural tendency to try to enrich it in a way that turns it into a cooperative, resolving answer.

In the case at hand, the relevant enrichment can be paraphrased as "No", meaning "No, I have never had a personal Swiss bank account. Intuitively, this is a Relevance-based implicature: Bronston appears to have given an answer that is no help at all in resolving the question (it is consistent with both "yes" and "no" answers), so we (more to the point, those assembled in the courtroom) seek to find a full resolution somewhere in the answer.

I believe the "No" enrichment can be derived as a conversational implicature:

    1. Contextual premise: people have exhaustive knowledge of their own personal bank accounts.
    2. Contextual premise: there is no entailment relationship between one's bank accounts and one's company's bank accounts.
    3. Bronston is cooperative, or at least abiding by Relevance. (Is this actually reasonable to assume in this adversarial context?)
    4. His answer is semantically irrelevant (leaves the prosecutor's question unresolved).
    5. It is not reasonable for Bronston to assume that his audience can get from his answer to an "I don't know" enrichment, given (a).
    6. It is not reasonable for Bronston to assume that his audience can get from his answer to a "yes" enrichment, given (b).
    7. This leaves "no", which, if assumed, makes the answer fully Relevance compliant (see (c)).

Comment: conversational implicatures are meanings that the speaker intends to send. It seems unlikely that Bronston intended to convey "no". If that were his intention, there would have been no motivation for being indirect! Thus, on a strict reading of the Gricean definition, the meaning is not an implicature.

Joshi's version of quality gets this right, it seems to me. It penalizes leaving one's listeners with misleading information. If Joshi were called as an expert witness, he would be able to articulate exactly why Bronston's dialogue act was misleading, whereas Grice would have to depart from his theory in order to characterize it.

Our experiment corpus happens to have an example. drawn from Hirschberg corpora, that is very much like the Bronston case:

    1. A: Do you belong to a gun club?
    2. B: My husband belonged to one awhile back.

In the next few sections, we will try to predict whether the answerer intended to convey "yes" or "no", and with how much certainty. Sometimes this enrichment is simply an entailment. In other cases, though, the answer is logically consistent with either "yes" or "no", but an inference in one direction or the other arises as a conversational implicature.

It's my hope that data-rich computational investigation sheds new light on these phenomena.


DERIVE State the likely conversational implicature of the gun-club example above and calculate that implicature using a set of maxims and a definition of conversational implicature. If you depart from Grice's maxims or Grice's original definition of implicature, explain why.

POLITENESS Provide an example in which politeness plays a central role in blocking an implicature or in creating one.

INDEF It’s common to knock on the door of a locked public restroom and hear (a) uttered from inside the restroom. Use Grice’s maxims to explain why this response is favored over each of (b) and (c). Also: What is odd about (a) in light of the maxims? (This problem is inspired by Mark Liberman's 2007 Language Log post Grice in the ladies' room.)

  1. "Someone's in here!"
  2. "X is in here!" (where X is the speaker’s name)
  3. "Albania's chief export is chrome!" (or something else arbitrary in the language of the speech community)

PROBE Use the extended definition of conversational implicature to evaluate the hypothesis that (a) conversationally implicates that some students did not do the homework. (Assume that the domain of relevant students is clear and fixed.)

  1. Almost every student did the homework.

If you get conflicting results from applying the definition's clauses, articulate where the conflicts lie and perhaps venture an explanation for them.

(For discussion of almost and implicature see Sadock 1978.)

SUSPENDERS Hirschberg (1985: 117-119) discusses Horn's (1972, 1989) claim that the connective if not, as in warm if not hot, functions to help the speaker ensure that the hearer does not draw an upper-bounding implicature from the first predicate — the second predicate opens up the possibility (but does not assert) that something stronger than the first predicate holds.

The following file contains all the 4-grams of word-like objects from the Google N-grams corpus in which words 2 and 3 are if not. Use this file to inform Horn's generalization, by assessing how often terms 1 and 4 are in a scalar relationship

For additional relevant discussion, see Hearst 1992 and Snow et al. 2005.

Reveal/Hide a partial solution

The following Python code compares w1 and w4 in the n-grams data using IMDB review scores (where we have data on adjectival realizations of those strings):

The output is a CSV file ifnot-cmps.csv that permits many different kinds of comparisons. Notes on the values:

BRONSTON The "No" inference for the Bronston example above seems fairly natural given default contextual assumptions, but it is far from inevitable. Replace the contextual assumptions given with some that would likely deliver a "yes" inference, and describe a path for arriving at that inference.