33. Implicature and presupposition

Much of what an English sentence conveys is neither said outright nor entailed: Some of the guests left suggests that not all did, She stopped crying takes for granted that she had been crying, and She opened the door and walked in is understood in that order. This chapter describes conversational and conventional implicature, scales, cancellation, presupposition triggers and their projection, accommodation, the probabilistic Rational Speech Acts account — and exactly what Mova's inference module computes, with its output on English examples and on a stretch of Alice's Adventures in Wonderland.

Contents

1. What is said, what is implicated, what is presupposed
2. The cooperative principle and the maxims
3. Kinds of implicature
4. Scalar implicatures
5. Other Quantity, Quality and Manner inferences
6. Presupposition
7. Projection and accommodation
8. Relevance theory and neo-Gricean views
9. Rational Speech Acts
10. Mova's inference module
11. Running it on a tale
12. Litotes, understatement and negation
13. Datasets

1. What is said, what is implicated, what is presupposed

The distinctions go back to Frege and Strawson for presupposition and to Grice for implicature (Grice 1975, "Logic and Conversation", not open — Wanted). Open surveys: Davis, "Implicature" (Stanford Encyclopedia of Philosophy, plato.stanford.edu/entries/implicature) and Beaver, Geurts & Denlinger, "Presupposition" (SEP, plato.stanford.edu/entries/presupposition). The overview of meaning layers is in 30 §2.

2. The cooperative principle and the maxims

Grice proposed that conversation is governed by a Cooperative Principle — make your contribution such as is required, at the stage at which it occurs, by the accepted purpose of the exchange — spelled out in four maxims (Grice 1975, as summarised in Davis, SEP):

When a maxim is flouted — blatantly broken — the hearer infers a meaning that restores cooperation: tautologies (Boys will be boys), irony (Quality, 34), hyperbole, deliberately vague answers.

3. Kinds of implicature

Conversational implicatures are cancellable (Some, in fact all, of the tarts were stolen), non-detachable (another wording with the same content keeps them), and calculable (a reasoning path from the maxims leads to them). Conventional implicatures are not cancellable: She is poor but honest — and there's no contrast is odd (Davis, SEP). The meaning of but is treated as a discourse relation (Comparison/Contrast) in 36.

4. Scalar implicatures

4.1 Horn scales

Many English words form scales ordered by informational strength (Horn 1972/1989, not open — Wanted): if the stronger term holds, the weaker one does too. Using the weaker term implicates that the speaker is not in a position to use the stronger one.

Mova's inference module (prag/src/infer.rs, SCALES) contains exactly these 17 scales, weakest first, matched on lemmas:

4.2 When the implicature does not arise

The module blocks a scalar implicature when (all from prag/src/infer.rs):

(1) «Mova 0.4, CPU, 2026-10-17», prag infer:

Some of the guests left.
  scalar implicature [Some]: not «all» (nor «many», «most») — «Some» is weaker than «all» on the scale
  some < many < most < all: a speaker who could say the stronger would have (Quantity)
It was warm in the hall.
  scalar implicature [warm]: not «hot» — «warm» is weaker than «hot» on the scale warm < hot …
It might rain.
  scalar implicature [might]: not «must» — «might» is weaker than «must» on the scale might < must …
He did not eat some of the tarts.
  (nothing: negated)
Some, in fact all, of the tarts were stolen.
  (nothing: cancelled by «in fact all»)
Most of the cakes were eaten, if not all.
  (nothing: cancelled by «if not all»)

4.3 Embedded implicatures

Whether scalar implicatures arise inside embedded positions (Every student read some of the books) is debated between "grammatical" and "pragmatic" theories; Potts, Lassiter, Levy & Frank (2016, "Embedded implicatures as pragmatic inferences under compositional lexical uncertainty", Journal of Semantics 33(4), potts-2016-embedded-implicatures-pragmatic-inferences-under) model them within RSA (§9). Mova computes implicatures per sentence and does not distinguish embedded from root occurrences, except under negation.

5. Other Quantity, Quality and Manner inferences

Tatu & Moldovan (2012, "A Tool for Extracting Conversational Implicatures", LREC, aclanthology.org/L12-1039, tatu-2012-tool-extracting-conversational-implicatures) implemented Grice's maxims as 63 hand-written axioms over logical forms with an abductive reasoner, reaching P 75.8 / R 65.8 / F 70.4 on Twitter conversations (Pragmatics: algorithms from the literature, for Mova (2026-10-03)). Mova takes four of their axioms as rules (prag/src/infer.rs, maxims):

The Manner rule's exceptions are listed in the code: stative verbs (STATIVE: be, have, know, like, love, own, believe, want, need, seem, belong, contain — states do not follow each other) and reordering words (REORDER: after, before, while, meanwhile, simultaneously, afterwards, beforehand, previously, earlier; then blocks the rule unless it sits on the second verb).

(2) «Mova 0.4, CPU, 2026-10-17»:

The fox ate the grapes and ran away.
  manner implicature [and]: «ate» happened before «ran» — two events «ate» and «ran» joined by «and» are told
  in the order they happened (Manner: be orderly); no stative verb, no reordering word
She walked in after she opened the door.
  (nothing: «after» reorders)
Did the crow sing again?
  quality implicature [?]: the speaker does not know whether «the crow sing again» — a yes/no question with
  the inverted «did»: a truthful speaker asks only what he does not know (Quality)

The same "be orderly" reasoning gives the next links of frames: and, then and sentence order link event frames in told order (36; Pragmatics: frames — who did what to whom, why, and what came next, Links). The Quality rule for questions is also what the dialogue layer uses: a member asked a question answers what it knows and says what it does not (Pragmatics: algorithms from the literature, for Mova (2026-10-03), What goes first).

Relation (relevance) inferences — Hungry? — I'm starving. — are not computed; indirect answers are the subject of the Circa dataset (§13).

6. Presupposition

6.1 Triggers

A presupposition is information a sentence takes for granted; it survives when the sentence is negated, questioned or made conditional. English presupposition triggers (Beaver, Geurts & Denlinger, SEP; Levinson 1983, Pragmatics, ch. 4 — not open, Wanted):

The adverb triggers too, again, also, still, yet were studied as a prediction task by Cianflone, Feng, Kabbara & Cheung (2018, "Let's do it 'again': A First Computational Approach to Detecting Adverbial Presupposition Triggers", ACL, aclanthology.org/P18-1256 our card, papers/c/ci/cianflone-2018-let-s-do-it-again): the cue for an adverb is a repeated event or entity in the preceding context; a bigram logistic regression is near chance except for too and yet, and an attention model reaches 76% on their Penn Treebank corpus (Pragmatics: algorithms from the literature, for Mova (2026-10-03)).

6.2 What Mova computes

For each trigger, prag/src/infer.rs (presuppositions) builds the content from the tree:

6.3 Licensing

A presupposition is licensed when the earlier text — up to 50 tokens back — contains the same predicate lemma; otherwise it is new information that the hearer must accommodate, and the output says so. The window and the same-predicate test follow Cianflone et al.'s observation that the cue is a repeated event in the context (Pragmatics: algorithms from the literature, for Mova (2026-10-03)).

(3) «Mova 0.4, CPU, 2026-10-17»:

The crow sang a song.
Then the crow sang again.
  presupposition [again]: «sing» happened before — «again» needs it, and the earlier text has «sing»
Did the crow sing again?          (as a first sentence)
  presupposition [again]: «sing» happened before (new) — «again» needs it, but the earlier text has no
  «sing»: the hearer must accommodate it as new
The fox came too.
  presupposition [too]: someone or something else «come» too (new) — …
The box is too heavy.
  (nothing: the excess «too» on an adjective is not additive)
She stopped crying.
  presupposition [stopped]: «cry» was going on before (new) — …
Alice knew that the door was locked.
  presupposition [knew]: it is true that «the door was locked» (new) — …

7. Projection and accommodation

7.1 Projection

Presuppositions project from embedded positions where entailments do not: Alice did not know that the door was locked, Did Alice know…?, If Alice knew…, she… all still presuppose that the door was locked. Karttunen (1973, "Presuppositions of compound sentences", Linguistic Inquiry 4 — Wanted) classified embedding contexts as holes (let presuppositions through: negation, questions, modals), plugs (block them: verbs of saying, believe) and filters (block them under conditions: if A then B filters B's presupposition when A entails it — If Alice has a cat, her cat is black). The SEP survey describes the later dynamic and DRT accounts (Beaver, Geurts & Denlinger, SEP).

Mova's module has no projection logic of its own: a trigger produces its presupposition wherever it occurs, which is right for holes (negation and questions) and wrong for plugs and filters. In practice the parser decides first. In (4) the trigger is in a hole, but the parser attaches the complement clause as advcl, so no presupposition is produced at all:

(4) «Mova en 0.4, CPU, 2026-10-17»:

Alice did not know that the Queen was angry.   advcl(know, angry)   → no presupposition
Did Alice regret that she had come?            advcl(regret, come)  → no presupposition
Alice knew that the door was locked.           ccomp(knew, locked)  → «the door was locked» is true

The UD analysis of all three is ccomp (23). This is a parser error with a pragmatic cost — a reminder that every pragmatic reading in Mova starts from the tree.

7.2 Accommodation

When a presupposition is not in the common ground, cooperative hearers usually add it silently — I have to pick up my sister is fine to someone who did not know about the sister (Lewis 1979, "Scorekeeping in a language game" — Wanted; Beaver, Geurts & Denlinger, SEP). Mova does not refuse unlicensed presuppositions; it marks them (new) with the explanation "the hearer must accommodate it as new". In a story reader this is useful: an unlicensed again or still points to an event the text has not told, a gap in the world of the story.

8. Relevance theory and neo-Gricean views

Relevance theory (Sperber & Wilson 1986/1995, Relevance: Communication and Cognition — not open, Wanted) replaces the maxims with one cognitive principle: an utterance creates an expectation of optimal relevance — enough effect to be worth the effort of processing. Implicatures are derived by mutual adjustment of explicit content, context and conclusions; much of what Grice called implicature (enrichment of and to and then, the resolution of some) is treated as part of the explicit content, the explicature. The neo-Gricean line (Horn's Q- and R-principles; Levinson 2000, Presumptive Meanings — Wanted) reduces the maxims to two or three heuristics and stresses generalised, default implicatures. Mova's rules follow the neo-Gricean, default style (§5): they fire without looking at the wider context, and context can only block them (negation, cancellation, reordering words).

9. Rational Speech Acts

9.1 The model

The Rational Speech Acts (RSA) framework models Gricean reasoning as recursive probabilistic inference between a speaker and a listener (Frank & Goodman 2012, "Predicting Pragmatic Reasoning in Language Games", Science 336(6084):998, doi.org/10.1126/science.1218633, frank-2012-predicting-pragmatic-reasoning-language-games; Goodman & Frank 2016, "Pragmatic Language Interpretation as Probabilistic Inference", Trends in Cognitive Sciences 20(11), doi.org/10.1016/j.tics.2016.08.005, goodman-2016-pragmatic-language-interpretation-probabilistic-inference):

Monroe & Potts (2015, "Learning in the Rational Speech Acts Model", arXiv:1510.06807, monroe-2015-learning-rational-speech-acts-model) learn the speaker's features from data; on the TUNA referring-expression corpus a learned RSA beats plain RSA (accuracy 25.3% vs 2.2%, Dice .777 vs .386, as summarised in Pragmatics: algorithms from the literature, for Mova (2026-10-03)).

9.2 Mova's exact RSA

prag/src/rsa.rs computes RSA over small closed sets exactly: α is a small positive integer, costs are whole bits, priors positive integers, so S1 ∝ L0^α · 2^(−α·C) and every value is a reduced fraction (u128 with gcd reduction; overflow fails loudly instead of rounding). Worlds and utterances keep their given order and ties go to the lowest index. The L0/S1/L1 rows are printed as the explanation.

(5) The scalar game, prag rsa scalar, «Mova 0.4, CPU, 2026-10-17» (worlds none, some-not-all, all; utterances none, some, all; uniform priors, α = 1, no costs):

"some" (cost 0, alpha 1), true of: some-not-all, all
  none             prior 1    L0 0 (0.0%)      S1 0 (0.0%)        L1 0 (0.0%)
  some-not-all     prior 1    L0 1/2 (50.0%)   S1 1 (100.0%)      L1 3/4 (75.0%)
  all              prior 1    L0 1/2 (50.0%)   S1 1/3 (33.3%)     L1 1/4 (25.0%)
  → some-not-all (L1 3/4; literal L0 1/2)

The literal listener cannot choose between some-not-all and all (1/2 each); the pragmatic listener reasons that a speaker in the all world would more likely have said all, and reaches 3/4 for not all — the scalar implicature as a probability. With a cost of 2 bits on all the implicature weakens to 3/5, and with α = 2 then to 5/9 (Pragmatics: algorithms from the literature, for Mova (2026-10-03)).

(6) The reference game of Frank & Goodman, prag rsa reference: a blue square, a blue circle and a green square; L1(blue) gives the blue square 3/5 and the blue circle 2/5 — blue points to the square because a speaker meaning the circle could have said circle; L1(square) gives 3/5 to the blue square. Negative control: utterances true of every world return the prior unchanged (prag/src/rsa.rs tests).

RSA is not yet connected to the sentence reader: it runs on hand-specified games. Its role in Mova is the explained, exact reference model against which the rule-based implicatures can be checked.

10. Mova's inference module

10.1 What it is

prag infer <en model> "<text>" parses the text with the en model and prints, per sentence, the scalar implicatures, presuppositions with their licensing, the Quality and Manner inferences, and irony candidates (34). Each inference has a kind, the trigger word, the content, a reason, and (for presuppositions) whether it was licensed (prag/src/infer.rs, struct Inference). It is deterministic; its tests include negative controls (a stronger item, negation, cancellation, stative verbs, reordering words) (Pragmatics: algorithms from the literature, for Mova (2026-10-03), Done (2026-10-03)).

10.2 What it gets wrong

Matching lemmas without the word's function overgenerates. On sentences from Alice («Mova 0.4, CPU, 2026-10-17»):

Each error has a structural fix that the tree supports: require the scale item's UPOS (like as VERB, most as DET or ADV of quantity, not advmod of an adjective), exclude fixed expressions (a good deal, should like) through the expression base (prag/src/lens.rs), and read stop + xcomp with to as purpose (prag/src/frames.rs already treats to-infinitives that are not control complements as purposes).

11. Running it on a tale

prag infer was run on 400 sentences of Alice's Adventures in Wonderland (book:pg11:* in the parse database, in database order — not reading order — so licensing counts are a lower bound) on 2026-10-17:

Two observations. First, again dominates the presuppositions: in a story, again links an event to an earlier one, which is exactly the next structure the story reader keeps (36). Second, like is the most frequent scalar trigger only because of the preposition and the should like formula (§10.2) — the count is a measure of the errors as much as of the phenomenon.

12. Litotes, understatement and negation

Litotes affirms by denying the opposite: This is not unknown to New Delhi (EWT 2.18 weblog-blogspot.com_dakbangla_20050210141134_ENG_20050210_141134-0021) means it is known, with a hedge or an emphasis that a plain known lacks; not bad is usually weaker praise than good, while not uncommon is "fairly common". The tree shows one negation and one negative affix; the meaning combines them (27, §11). Horn's account (A Natural History of Negation, 1989 — Wanted) explains the weakening as an R-based implicature: the speaker chose the longer, marked form, so a marked meaning is intended (Manner).

Understatement (meiosis) says less than is meant: It's a bit chilly in a snowstorm; I was not entirely pleased. It flouts Quantity in the direction opposite to hyperbole and is a common vehicle of British irony (34).

Negative questions carry a bias: Can you not understand that? (book:pg1597:1669) expects yes and reproaches; Isn't it lovely? invites agreement. The experimental and theoretical work on such biased questions is collected in Trinh, Benz, Goodhue, Yatsushiro & Krifka (eds.) 2025, Biased questions: Experimental results and theoretical modelling, Language Science Press, books/k/kr/krifka-2025-biased-questions-experimental-results (26).

In Mova, scalar implicatures are blocked under negation (§4.2); litotes and negative-question bias are not computed. The polarity label of prag.tsv is the speaker's evaluation, not grammatical negation (30 §6; 27).

13. Datasets

All of the following are for tests and measurements only, under their own licences (Data and model licences in the repo; English pragmatics tools — local collection):

Jeretic et al. report that BERT trained on MultiNLI reliably treats the scalar implicature of some as an entailment and recognises some presupposition triggers such as only, though MultiNLI contains very few such pairs — useful as a point of comparison for Mova's rule-based output, which states its inference and its reason instead of a label.

In Mova

• Implicatures, presuppositions, Quality and Manner: prag/src/infer.rs (SCALES, implicatures, presuppositions, maxims, STATIVE, REORDER); CLI prag infer <en model> "<text>".
• Exact RSA: prag/src/rsa.rs; CLI prag rsa scalar|reference.
• Told order as frame links (next): prag/src/frames.rs; design: Pragmatics: algorithms from the literature, for Mova (2026-10-03), Pragmatics: frames — who did what to whom, why, and what came next.
• Not yet:
  • no projection logic (holes, plugs, filters) — a trigger fires wherever the parser shows it with the right relation, and not at all when the parser mislabels the complement (§7.1);
  • scale items are matched by lemma without their part of speech or function (§10.2);
  • Relation inferences (indirect answers), clausal implicatures, conventional implicatures of but, even, only, and presuppositions of definites, clefts, possessives, wh-questions and temporal clauses are not computed;
  • the inferences are printed, not stored: they do not enter frames, the world or the student's answers;
  • RSA runs on hand-specified games only.

Sources

• Grice, H. P. 1975. Logic and Conversation. Not open — Wanted.
• Horn, L. R. 1972. On the Semantic Properties of Logical Operators in English; 1989. A Natural History of Negation. Not open — Wanted.
• Karttunen, L. 1973. Presuppositions of compound sentences. Linguistic Inquiry 4. Not open — Wanted.
• Lewis, D. 1979. Scorekeeping in a language game. Journal of Philosophical Logic 8. Not open — Wanted.
• Levinson, S. C. 1983. Pragmatics; 2000. Presumptive Meanings. Not open — Wanted.
• Sperber, D., Wilson, D. 1986/1995. Relevance: Communication and Cognition. Not open — Wanted.
• Davis, W. "Implicature". Stanford Encyclopedia of Philosophy. plato.stanford.edu/entries/implicature
• Beaver, D. I., Geurts, B., Denlinger, K. "Presupposition". Stanford Encyclopedia of Philosophy. plato.stanford.edu/entries/presupposition
• Tatu, M., Moldovan, D. 2012. A Tool for Extracting Conversational Implicatures. LREC. aclanthology.org/L12-1039; tatu-2012-tool-extracting-conversational-implicatures
• Cianflone, A., Feng, Y., Kabbara, J., Cheung, J. C. K. 2018. Let's do it "again": A First Computational Approach to Detecting Adverbial Presupposition Triggers. ACL. aclanthology.org/P18-1256 our card; papers/c/ci/cianflone-2018-let-s-do-it-again
• Frank, M. C., Goodman, N. D. 2012. Predicting Pragmatic Reasoning in Language Games. Science 336(6084):998. doi.org/10.1126/science.1218633; frank-2012-predicting-pragmatic-reasoning-language-games
• Goodman, N. D., Frank, M. C. 2016. Pragmatic Language Interpretation as Probabilistic Inference. Trends in Cognitive Sciences 20(11). doi.org/10.1016/j.tics.2016.08.005; goodman-2016-pragmatic-language-interpretation-probabilistic-inference
• Monroe, W., Potts, C. 2015. Learning in the Rational Speech Acts Model. arXiv:1510.06807. monroe-2015-learning-rational-speech-acts-model
• Potts, C., Lassiter, D., Levy, R., Frank, M. C. 2016. Embedded implicatures as pragmatic inferences under compositional lexical uncertainty. Journal of Semantics 33(4). potts-2016-embedded-implicatures-pragmatic-inferences-under
• Jeretic, P., Warstadt, A., Bhooshan, S., Williams, A. 2020. Are Natural Language Inference Models IMPPRESsive? Learning IMPlicature and PRESupposition. ACL. aclanthology.org/2020.acl-main.768 our card; papers/j/je/jeretic-2020-are-natural-language-inference-models
• Louis, A., Roth, D., Radlinski, F. 2020. "I'd rather just go to bed": Understanding Indirect Answers. EMNLP. aclanthology.org/2020.emnlp-main.601 our card; louis-2020-i-d-rather-just-go
• Zheng, Z., Qiu, S., Fan, L., Zhu, Y., Zhu, S.-C. 2021. GRICE: A Grammar-based Dataset for Recovering Implicature and Conversational rEasoning. Findings of ACL. aclanthology.org/2021.findings-acl.182 our card
• Trinh, T., Benz, A., Goodhue, D., Yatsushiro, K., Krifka, M. (eds.) 2025. Biased questions: Experimental results and theoretical modelling. Language Science Press. books/k/kr/krifka-2025-biased-questions-experimental-results
• UD English EWT 2.18 (CC BY-SA 4.0), sentences cited by sent_id.
• Mova's parse database (current.conllu): Alice's Adventures in Wonderland (pg11), Andersen's Fairy Tales (pg1597); runs of prag infer and prag rsa with the release 0.4 model, 2026-10-17.
• Repo: Pragmatics: algorithms from the literature, for Mova (2026-10-03), Pragmatics: frames — who did what to whom, why, and what came next.

This page in Markdown → https://md.mova.elamur.ai/free/en/docs/languages/en/33-implicature-and-presupposition/