---
title: "Conversational Implicatures: Modelling Relevance Theory"
description: "Peter offers coffee, and Mary replies that she avoids energizing drinks at this hour. 30 references."
authors: ["Christoph Unger", "Hendrik Buschmeier"]
year: 2025
venue: "arXiv:2509.22354"
source: "https://arxiv.org/abs/2509.22354"
doi: "10.48550/arxiv.2509.22354"
arxiv: "2509.22354"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/unger-2025-conversational-implicatures-modelling-relevance-theory/"
---
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# Conversational Implicatures: Modelling Relevance Theory Probabilistically

**Authors:** Christoph Unger and [Hendrik Buschmeier](https://md.research.elamur.ai/free/en/authors/hendrik-buschmeier/) · **Year:** 2025 · **Venue:** arXiv:2509.22354 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2509.22354) · [PDF](https://arxiv.org/pdf/2509.22354) · [DOI 10.48550/arxiv.2509.22354](https://doi.org/10.48550/arxiv.2509.22354) · [arXiv 2509.22354](https://arxiv.org/abs/2509.22354) · [OpenAlex](https://openalex.org/W7083674616)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
The paper asks whether relevance theory (Sperber & Wilson), which is usually stated informally, can be given a Bayesian treatment similar to what Rational Speech Act theory provides for Gricean pragmatics. The authors focus on conversational implicatures, using a running example. Peter offers coffee, and Mary replies that she avoids energizing drinks at this hour. They separate the explicature (the enriched, reference-resolved proposition) from the implicit premise and the implicit conclusion. Comprehension is then built in ProbLog. Each interpretive hypothesis is a probabilistic logic program combining the utterance with background knowledge. Cognitive effect is measured as the KL divergence between prior and posterior probabilities of relevant assumptions. Processing effort is approximated by the size of the program's Herbrand base. The result is an "as-if" optimization procedure that picks the interpretation a relevance-guided hearer should arrive at, which yields quantitative predictions that experiments could test. Candidate hypotheses are still written by hand, and only the hearer's side is modelled.

## Key points
- The model is built using ProbLog, a language that combines logic programming with probabilities. Its world knowledge covers beverages such as coffee, coke, tea, fruitTea, peppermintTea, redBull, proteinShake and water, encoded through `wantsNotDrink(mary, X)` atoms.
- Cognitive effect is computed as summed per-assumption KL divergence between prior and updated probabilities. For example, Int 1 and Int 4 both total 2.3472.
- Int 4 adds an extra encyclopaedic knowledge graph without raising the KL score. It therefore has a larger Herbrand base, read as more effort for no extra benefit.
- Int 5 adds `healthconscious(mary)`, which moves from a prior of 0.50 to roughly 0.82. This raises the total KL to 2.4207, so the extra effort pays off.
- The selection procedure has three steps:
  - Drop hypotheses that fail any relevance expectation (e.g. Int 2).
  - Among KL ties, prefer the smallest Herbrand base.
  - Take the hypothesis with the highest KL.

## Interesting ideas
- Treat each candidate reading of an utterance as a separate small knowledge program and score it by how much it shifts beliefs, rather than by surface similarity; this makes the choice of interpretation inspectable step by step.
- Use KL divergence between prior and posterior over a fixed set of query propositions as a numeric stand-in for "cognitive effect"; it gives a single comparable score while keeping per-proposition contributions visible.
- Approximate processing cost by the number of facts/atoms an interpretation needs, using it only as a tie-breaker when benefit is equal; this is a cheap, transparent proxy for Occam-style preference.
- Structure interpretation as a lexicographic filter: first enforce hard constraints (the reply must answer the question), then minimize effort among ties, then maximize effect. This ordering is easy to explain and debug compared with one weighted sum.
- Explicitly separate the explicature (reference-resolved, time-resolved proposition) from implicit premises and conclusions, so bridging background assumptions are first-class objects rather than hidden.

## For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

- **I1** (frames): prag could generate competing implicature hypotheses (e.g. "she declines coffee") and record, for each, which belief updates justified picking it.
- **I2** (world): when a sentence updates the text world, the per-entity/per-state probability shifts could be logged as an explainable "informativeness" score for that sentence.
- **I3** (world): when several knowledge-graph expansions (WordNet/Wikidata facts) explain the same inference, prefer the one pulling in fewer facts, and report the count.
- **I4** (answer): QA readers could reject answers that fail the question's expectation before ranking the rest by supporting-evidence size and strength.
- **I5** (frames): implicature output could store the supplied premise (e.g. "coffee is an energizing drink") as a separate, traceable node linked to the frame it completes.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Christoph Unger and Hendrik Buschmeier. 2025. Conversational Implicatures: Modelling Relevance Theory Probabilistically. arXiv:2509.22354.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{unger2025conversational,
  title = {{Conversational Implicatures: Modelling Relevance Theory Probabilistically}},
  author = {Christoph Unger and Hendrik Buschmeier},
  year = {2025},
  doi = {10.48550/arxiv.2509.22354},
  eprint = {2509.22354},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2509.22354}
}
```

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## References

30 references, 1 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Beaver, David I., Craige Roberts, Mandy Simons and Judith Tonhauser (2017). ‘Questions Under Discussion: Where Information Structure Meets Projective Content’. In: Annual Review of Linguistics 3, pp. 265–284. doi: 10.1146/annurev-linguistics-011516-033952. [↗](https://doi.org/10.1146/annurev-linguistics-011516-033952)
2. Bergen, Leon, Roger Levy and Noah D. Goodman (2016). ‘Pragmatic Reasoning through Semantic Inference’. In: Semantics and Pragmatics 9.20, pp. 1–91. url: http://semprag.org/article/view/sp.9.20. [↗](https://doi.org/10.3765/sp.9.20)
3. Carston, R. (1995). ‘Quantity Maxims and Generalised Implicature’. In: Lingua 96, pp. 213–244. doi: 10.1016/0024-3841(95)00016-S. [↗](https://doi.org/10.1016/0024-3841(95)00016-s)
4. Carston, Robyn (1988). ‘Implicature, Explicature, and Truth-Theoretic Semantics’. In: Mental Representations. Ed. by Ruth Kempson. Cambridge, UK: Cambridge University Press, pp. 155–182. [find](https://scholar.google.com/scholar?q=Carston%2C+Robyn+%281988%29%2E+%E2%80%98Implicature%2C+Explicature%2C+and+Truth%2DTheoretic+Semantics%E2%80%99%2E+In%3A+Mental+Representations%2E+Ed%2E+by+Ruth+Kempson%2E+Cambridge%2C+UK%3A+Cambridge+University+Press%2C+pp%2E+155%E2%80%93182%2E)
5. Carston, Robyn (2002). Thoughts and Utterances. Oxford, UK: Blackwell. [find](https://scholar.google.com/scholar?q=Carston%2C+Robyn+%282002%29%2E+Thoughts+and+Utterances%2E+Oxford%2C+UK%3A+Blackwell%2E)
6. Clark, Billy (2013). Relevance Theory. Cambridge, UK: Cambridge University Press. [find](https://scholar.google.com/scholar?q=Clark%2C+Billy+%282013%29%2E+Relevance+Theory%2E+Cambridge%2C+UK%3A+Cambridge+University+Press%2E)
7. Degen, Judith (2023). ‘The Rational Speech Act Framework’. In: Annual Review of Linguistics 9.1, pp. 519–540. doi: 10 . 1146 / annurev - linguistics - 031220 -010811. [↗](https://doi.org/10.1146/annurev-linguistics-031220-010811)
8. Erk, Katrin (2022). ‘The Probabilistic Turn in Semantics and Pragmatics’. In: Annual Review of Linguistics 8.1, pp. 101–121. doi: 10 . 1146 / annurev - linguistics -031120-015515. Erk, Katrin and Aurélie Herbelot (2023-11-30). ‘How to Marry a Star: Probabilistic Constraints for Meaning in Context’. In: Journal of Semantics 40.4, pp. 549–583. doi: 10.1093/jos/ffad016. [↗](https://doi.org/10.1093/jos/ffad016)
9. Fierens, Daan, Guy Van Den Broeck, Joris Renkens, Dimitar Shterionov, Bernd Gutmann, Ingo Thon, Gerda Janssens and Luc De Raedt (2015). ‘Inference and Learning in Probabilistic Logic Programs Using Weighted Boolean Formulas’. In: Theory and Practice of Logic Programming 15.3, pp. 358–401. doi: 10.1017/S1471068414000076. [↗](https://doi.org/10.1017/s1471068414000076)
10. Flach, Peter (1994). Simply Logical: Intelligent Reasoning by Example. John Wiley. url: [http://people.cs.bris.ac.uk/~flach/index.html](http://people.cs.bris.ac.uk/~flach/index.html). [↗](http://people.cs.bris.ac.uk/~flach/index.html)
11. Frank, Michael C. and Noah D. Goodman (2012). ‘[Predicting Pragmatic Reasoning in Language Games](https://md.research.elamur.ai/free/en/papers/frank-2012-predicting-pragmatic-reasoning-language-games/)’. In: Science 336.6084, pp. 998–998. doi: 10.1126/science. 1218633. [↗](https://doi.org/10.1126/science)
12. Gigerenzer, Gerd (2004). ‘Fast and Frugal Heuristics: The Tools of Bounded Rationality’. In: Blackwell Handbook of Judgment and Decision Making 62, p. 88. [↗](https://doi.org/10.1002/9780470752937.ch4)
13. Goodman, Noah D. and Michael C. Frank (2016). ‘Pragmatic Language Interpretation as Probabilistic Inference’. In: Trends in Cognitive Sciences 20.11, pp. 818–829. doi: 10.1016/j.tics.2016.08.005. [↗](https://doi.org/10.1016/j.tics.2016.08.005)
14. Goodman, Noah D. and Andreas Stuhlmüller (2013). ‘Knowledge and Implicature: Modeling Language Understanding as Social Cognition’. In: Topics in Cognitive Science 5.1, pp. 173–184. doi: 10.1111/tops.12007. [↗](https://doi.org/10.1111/tops.12007)
15. Grice, H. Paul (1957). ‘Meaning’. In: The Philosophical Review 66.3, pp. 377–388. doi: 10.2307/2182440. [↗](https://doi.org/10.2307/2182440)
16. Grice, H. Paul (1967). ‘William James Lectures’. [find](https://scholar.google.com/scholar?q=Grice%2C+H%2E+Paul+%281967%29%2E+%E2%80%98William+James+Lectures%E2%80%99%2E)
17. Grice, H. Paul (1989). Studies in the Way of Words. Cambridge, MA, USA: Harvard University Press. [find](https://scholar.google.com/scholar?q=Grice%2C+H%2E+Paul+%281989%29%2E+Studies+in+the+Way+of+Words%2E+Cambridge%2C+MA%2C+USA%3A+Harvard+University+Press%2E)
18. Horn, Laurence R. (1984). ‘Towards a New Taxonomy of Pragmatic Inference: Q-based and R-based Implicature’. In: Meaning, Form, and Use in Context: Linguistic Applications. Ed. by Deborah Schiffrin. Washington, DC, USA: Georgetown University Press, pp. 11–42. [find](https://scholar.google.com/scholar?q=Horn%2C+Laurence+R%2E+%281984%29%2E+%E2%80%98Towards+a+New+Taxonomy+of+Pragmatic+Inference%3A+Q%2Dbased+and+R%2Dbased+Implicature%E2%80%99%2E+In%3A+Meaning%2C+Form%2C+and+Use+in+Context%3A+Linguistic+Applications%2E+Ed%2E+by+Deborah+Schiffrin%2E+Wa)
19. Mansinghka, Vikash Kumar (2009). ‘Natively Probabilistic Computation’. PhD thesis. Cambridge, MA, USA: MIT. url: [http://web.mit](http://web.mit) . edu / vkm / www / vkm -dissertation.pdf. [↗](http://web.mit)
20. Scontras, Gregory, Michael Henry Tessler and Michael Franke (n.d.). Probabilistic Language Understanding: An Introduction to the Rational Speech Act Framework. url: [http://www.problang.org/](http://www.problang.org/). Sperber, Dan and Deirdre Wilson (1995). Relevance. 2nd ed. Oxford, UK: Blackwell. [↗](http://www.problang.org/)
21. Sperber, Dan and Deirdre Wilson (1998). ‘The Mapping between the Mental and the Public Lexicon’. In: Language and Thought. Ed. by Peter Carruthers and Jill Boucher. Cambridge, UK: Cambridge University Press, pp. 184–200. [↗](https://doi.org/10.1017/cbo9780511597909.012)
22. Sperber, Dan and Deirdre Wilson (2015). ‘Beyond Speaker’s Meaning’. In: Croation Journal of Philosophy XV.44, pp. 117–149. [find](https://scholar.google.com/scholar?q=Sperber%2C+Dan+and+Deirdre+Wilson+%282015%29%2E+%E2%80%98Beyond+Speaker%E2%80%99s+Meaning%E2%80%99%2E+In%3A+Croation+Journal+of+Philosophy+XV%2E44%2C+pp%2E+117%E2%80%93149%2E)
23. Tenenbaum, Joshua B., Thomas L. Griffiths and Charles Kemp (2006). ‘Theory-Based Bayesian Models of Inductive Learning and Reasoning’. In: Trends in Cognitive Sciences 10.7, pp. 309–318. doi: 10.1016/j.tics.2006.05.009. [↗](https://doi.org/10.1016/j.tics.2006.05.009)
24. Tenenbaum, Joshua B., Charles Kemp, Thomas L. Griffiths and Noah D. Goodman (2011). ‘How to Grow a Mind: Statistics, Structure, and Abstraction’. In: Science 331.6022, pp. 1279–1285. doi: 10.1126/science.1192788. [↗](https://doi.org/10.1126/science.1192788)
25. Tessler, Michael Henry, Joshua B. Tenenbaum and Noah D. Goodman (2022). ‘Logic, Probability, and Pragmatics in Syllogistic Reasoning’. In: Topics in Cognitive Science 14.3, pp. 574–601. doi: 10.1111/tops.12593. [↗](https://doi.org/10.1111/tops.12593)
26. Unger, Christoph (2006). Genre, Relevance and Global Coherence: The Pragmatics of Discourse Type. Basingstoke: Palgrave Macmillan. [find](https://scholar.google.com/scholar?q=Unger%2C+Christoph+%282006%29%2E+Genre%2C+Relevance+and+Global+Coherence%3A+The+Pragmatics+of+Discourse+Type%2E+Basingstoke%3A+Palgrave+Macmillan%2E)
27. Wilson, Deirdre and Dan Sperber (1991). ‘Inference and Implicature’. In: Pragmatics: A Reader. Ed. by Steven Davis. Oxford, UK: Oxford University Press, pp. 377–392. [find](https://scholar.google.com/scholar?q=Wilson%2C+Deirdre+and+Dan+Sperber+%281991%29%2E+%E2%80%98Inference+and+Implicature%E2%80%99%2E+In%3A+Pragmatics%3A+A+Reader%2E+Ed%2E+by+Steven+Davis%2E+Oxford%2C+UK%3A+Oxford+University+Press%2C+pp%2E+377%E2%80%93392%2E)
28. Wilson, Deirdre and Dan Sperber (2002). ‘Truthfulness and Relevance’. In: Mind 111, pp. 583–632. [↗](https://doi.org/10.1093/mind/111.443.583)
29. Wilson, Deirdre and Dan Sperber (2004). ‘Relevance Theory’. In: The Handbook of Pragmatics. Ed. by Laurence R. Horn and Gregory Ward. Oxford, UK: Blackwell, pp. 607–632. [find](https://scholar.google.com/scholar?q=Wilson%2C+Deirdre+and+Dan+Sperber+%282004%29%2E+%E2%80%98Relevance+Theory%E2%80%99%2E+In%3A+The+Handbook+of+Pragmatics%2E+Ed%2E+by+Laurence+R%2E+Horn+and+Gregory+Ward%2E+Oxford%2C+UK%3A+Blackwell%2C+pp%2E+607%E2%80%93632%2E)
30. Wilson, Deirdre and Dan Sperber (2012). Meaning and Relevance. Cambridge, UK: Cambridge University Press. 400 pp. [↗](https://doi.org/10.1017/cbo9781139028370)

*Updated 1 November 2026*