--- title: "From compositional semantics to Bayesian pragmatics via logical" description: "Montague-style formal semantics assigns precise meanings to sentences but has little to say about how context and… 3 references." authors: ["Julian Grove", "Jean-Philippe Bernardy", "Stergios Chatzikyriakidis"] year: 2021 venue: "Proceedings of the 1st and 2nd Workshops on Natural Logic Meets Machine Learning (NALOMA)" source: "https://aclanthology.org/2021.naloma-1.8/" licence: "CC BY 4.0 (ACL Anthology)" licence_url: "https://creativecommons.org/licenses/by/4.0/" summary_licence: "Elamur Cosmic License" canonical: "https://research.elamur.ai/free/en/papers/grove-2021-compositional-semantics-bayesian-pragmatics-logical/" --- [Elamur Research](https://md.research.elamur.ai/free/en/) · [this page in HTML](https://research.elamur.ai/free/en/papers/grove-2021-compositional-semantics-bayesian-pragmatics-logical/) [home](https://md.research.elamur.ai/free/en/) / [papers](https://md.research.elamur.ai/free/en/papers/) / [2021](https://md.research.elamur.ai/free/en/papers/2021/page/8/) / From compositional semantics to Bayesian pragmatics via logical inference # From compositional semantics to Bayesian pragmatics via logical inference **Authors:** Julian Grove, [Jean-Philippe Bernardy](https://md.research.elamur.ai/free/en/authors/jean-philippe-bernardy/) and [Stergios Chatzikyriakidis](https://md.research.elamur.ai/free/en/authors/stergios-chatzikyriakidis/) · **Year:** 2021 · **Venue:** [Proceedings of the 1st and 2nd Workshops on Natural Logic Meets Machine Learning (NALOMA)](https://md.research.elamur.ai/free/en/venues/naloma/) ([NALOMA 2021](https://md.research.elamur.ai/free/en/venues/naloma/2021/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/) **Links:** [Publisher's page](https://aclanthology.org/2021.naloma-1.8/) · [PDF](https://aclanthology.org/2021.naloma-1.8.pdf) ## Summary Montague-style formal semantics assigns precise meanings to sentences but has little to say about how context and background knowledge shape interpretation. Formal pragmatic models such as Rational Speech Act (RSA) predict meaning in context, yet they lack a well-defined compositional semantics. The authors bring the two together. Their interpreter turns a syntactic analysis into a probability distribution over first-order logic formulae. A set of random parameters θ selects among the possible readings, for example which antecedent a pronoun picks up. Background knowledge is modelled as a distribution over world-states, each a set of FOL formulae. Truth is checked with a depth-bounded tableau prover, which gives expected truth values. A variant of RSA, generalised to arbitrary propositions, then computes a posterior over meanings. All components are written as composable probabilistic programs in continuation-passing (monadic) style, staying within the simply typed λ-calculus. Applied to pronoun resolution in two scenarios with different priors, the model yields the expected antecedent preferences. Its output stays stable across reasonable parameter ranges. The work shows a principled way for lexical and world knowledge to steer disambiguation without giving up logical semantics. ## Key points - Pipeline: syntax → distribution over FOL formulae (parameterised by θ) → truth values via a FOL tableau prover capped at depth 10 → RSA refinement over meanings. Code is released on GitHub. - Literal listener: the probability of a reading is the expected chance that the world-state, the candidate proposition and the utterance's interpretation together do not derive a contradiction. - World knowledge can be continuous or discrete. Examples include a height drawn from a normal distribution (mean 1.8 m, sd 0.05 m) and sets of literals whose polarity is fixed by Bernoulli variables. - Differences from Lassiter and Goodman (2013): - The model infers utterance meanings rather than directly marginalising world-states. - The pragmatic speaker re-samples θ instead of keeping it fixed. - Unlike Goodman and Lassiter's Church implementation, probability is added without changing the metalanguage's semantics. - Limitations and future work: - Limitations: there are no syntactic binding constraints and no discourse or psycholinguistic factors in the anaphora model. - Future work: the authors plan to address vagueness and to evaluate on FraCaS, RTE and the probabilistic suite of Bernardy et al. (2019a). ## Interesting ideas - Treat each ambiguity as an explicit random parameter of the interpretation function, so the semantics outputs a weighted set of logical forms rather than committing early. - Score a candidate reading by whether it stays consistent with sampled background world-states, i.e. a contradiction check rather than a similarity score. - Bound the theorem prover's depth, both to sidestep undecidability and as a model of finite reasoning by agents. - Represent uncertain world knowledge as sets of literals whose truth is drawn from Bernoulli variables, plus continuous distributions for measures. - Check that model predictions remain stable when its free parameters (rationality exponent, costs, priors) are varied within plausible ranges. ## For Mova How these ideas could serve Mova, our small open language model — its files, stages and tests: - **I1** (frames): Pronoun antecedents and attachment choices could become named parameters in frame building, keeping alternative frames alive until world knowledge decides between them. - **I2** (world): Each candidate frame could be added to the text's world and rejected or down-weighted when it clashes with known states or holdings, which gives an explainable reason for the choice. - **I3** (answer): Readers answering test questions could run inference under a fixed depth budget, guaranteeing termination and short, inspectable proof traces. - **I4** (world): Uncertain knowledge-graph facts and measures (heights, prices) could carry such priors, so expected truth values replace hard yes/no lookups. - **I5** (learn): Evaluation could include parameter sweeps over tunable pragmatic weights, flagging answers that flip under small changes as fragile. *Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.* 📚 Shelves (2): [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 9,296 works · [🗣️ Language and Linguistics](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/language-and-linguistics/) · 9,206 works 🧭 Topics (1): [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 510 works ## Cite Cite as: Julian Grove, Jean-Philippe Bernardy and Stergios Chatzikyriakidis. 2021. From compositional semantics to Bayesian pragmatics via logical inference. Proceedings of the 1st and 2nd Workshops on Natural Logic Meets Machine Learning (NALOMA). The paper itself, not this page. BibTeX from the library's record of the work. ```bibtex @inproceedings{grove2021compositional, title = {{From compositional semantics to Bayesian pragmatics via logical inference}}, author = {Julian Grove, Jean-Philippe Bernardy and Stergios Chatzikyriakidis}, booktitle = {Proceedings of the 1st and 2nd Workshops on Natural Logic Meets Machine Learning (NALOMA)}, year = {2021}, url = {https://aclanthology.org/2021.naloma-1.8/} } ``` - [← previous Fisseha G. Demoze and William H. Armstrong. Ethiopian Amharic Proverbs](https://md.research.elamur.ai/free/en/papers/roamndo-2021-fisseha-g-demoze-william-h/) - [next → From polysemy to semantic change: remarks on the lexeme miṣwà in Biblical and Mishnaic Hebrew](https://md.research.elamur.ai/free/en/papers/vergari-2021-polysemy-semantic-change-remarks-lexeme/) - [↑ back to papers of 2021](https://md.research.elamur.ai/free/en/papers/2021/page/8/) ## References 3 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet. 1. Abzianidze, L. (2015). A Tableau Prover for Natural Logic and Language. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 2492–2502, Lisbon, Portugal. Association for Computational Linguistics. [find](https://scholar.google.com/scholar?q=Abzianidze%2C+L%2E+%282015%29%2E+A+Tableau+Prover+for+Natural+Logic+and+Language%2E+In+Proceedings+of+the+2015+Conference+on+Empirical+Methods+in+Natural+Language+Processing%2C+pages+2492%E2%80%932502%2C+Lisbon%2C+Portugal%2E+As) 2. Abzianidze, L. (2020). Learning as Abduction: Trainable Natural Logic Theorem Prover for Natural Language Inference. arXiv:2010.15909 [cs]. arXiv: 2010.15909. [↗](https://arxiv.org/abs/2010.15909) 3. Beltagy, I., Chau, C., Boleda, G., Garrette, D., Erk, K., and Mooney, R. (2013). Montague Meets Markov: Deep Semantics with Probabilistic Logical Form. In Second Joint Conference on Lexical and Computational Semantics (*SEM), Volume 1: Proceedings of the Main Conference and the Shared Task: Semantic Textual Similarity, pages 11–21, Atlanta, Georgia, USA. Association for Computational Linguistics. [find](https://scholar.google.com/scholar?q=Beltagy%2C+I%2E%2C+Chau%2C+C%2E%2C+Boleda%2C+G%2E%2C+Garrette%2C+D%2E%2C+Erk%2C+K%2E%2C+and+Mooney%2C+R%2E+%282013%29%2E+Montague+Meets+Markov%3A+Deep+Semantics+with+Probabilistic+Logical+Form%2E+In+Second+Joint+Conference+on+Lexical+and+Comput) *Updated 24 October 2026*