--- title: "Compositionality for Presuppositions over Tableaux (1995)" description: "The paper tackles a long-standing puzzle: how to compute the presuppositions of a compound statement built with if…then… 12 references." authors: ["Pablo Gervas"] year: 1995 venue: "arXiv:cmp-lg/9505014" source: "https://arxiv.org/abs/cmp-lg/9505014" doi: "10.48550/arxiv.cmp-lg/9505014" arxiv: "cmp-lg/9505014" licence: "arXiv non-exclusive distribution licence (read only, no redistribution)" licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/" summary_licence: "Elamur Cosmic License" canonical: "https://research.elamur.ai/free/en/papers/gervas-1995-compositionality-presuppositions-over-tableaux/" --- [Elamur Research](https://md.research.elamur.ai/free/en/) · [this page in HTML](https://research.elamur.ai/free/en/papers/gervas-1995-compositionality-presuppositions-over-tableaux/) [home](https://md.research.elamur.ai/free/en/) / [papers](https://md.research.elamur.ai/free/en/papers/) / [1995](https://md.research.elamur.ai/free/en/papers/1995/) / Compositionality for Presuppositions over Tableaux # Compositionality for Presuppositions over Tableaux **Authors:** [Pablo Gervas](https://md.research.elamur.ai/free/en/authors/pablo-gervas/) · **Year:** 1995 · **Venue:** arXiv:cmp-lg/9505014 · **Licence:** [arXiv non-exclusive distribution licence (read only, no redistribution)](http://arxiv.org/licenses/nonexclusive-distrib/1.0/) **Links:** [Publisher's page](https://arxiv.org/abs/cmp-lg/9505014) · [PDF](https://arxiv.org/pdf/cmp-lg/9505014) · [DOI 10.48550/arxiv.cmp-lg/9505014](https://doi.org/10.48550/arxiv.cmp-lg/9505014) · [arXiv cmp-lg/9505014](https://arxiv.org/abs/cmp-lg/9505014) · [OpenAlex](https://openalex.org/W1588671401) **Citations:** 0 citations (OpenAlex, 2026-10-14) ## Summary The paper tackles a long-standing puzzle: how to compute the presuppositions of a compound statement built with *if…then*, *and*, and *or* from the presuppositions of its atomic parts, without falling into the trap where presupposition-as-entailment makes every presupposition a tautology. Gervás represents sentences as propositional formulas and uses a modified tableau calculus in which the branching (β) rules list every truth-value combination explicitly rather than the minimal set of cases. This yields the Coverage Property: every atom appears, negated or not, on every open branch, so each branch behaves like a truth-table row that can be pruned when it becomes inconsistent. Two simple rules then decide presupposition. On a branch, a presupposition holds unless the branch already asserts it, asserts its negation, or contains a clashing presupposition. A whole tableau presupposes whatever its open branches presuppose. The rules reproduce the classic textbook judgments, including disjunction and context effects in discourse. The paper argues the method is better grounded than the accounts of Beaver, Mercer and van der Sandt. ## Key points - **Venue:** the workshop *Computational Logic for Natural Language Processing* (COMPULOG/ELSNET/EAGLES), Edinburgh, April 1995. - **Change to the calculus:** only the β-rules differ from standard semantic tableaux (ST). The resulting presuppositional tableaux (PT) are argued to close exactly when ST tableaux do, so PT still works as a decision method. - **Rule 1 (branch level):** a presupposition on an open branch survives unless one of three things is true: - the branch already asserts it; - the branch asserts its negation; - another atom on the branch presupposes its negation. - **Rule 2 (tableau level):** a tableau presupposes something if and only if an open branch does. By the Coverage Property, branches never disagree on this. - **Satisfaction and cancellation:** - A presupposition φ is *satisfied* when adding ¬φ closes the tableau. - It is *canceled* when adding φ closes it. - In hybrid cases, some branches close on φ and others on ¬φ. One example is a conditional whose antecedent states that a typewriter exists and whose consequent says that this typewriter is blue; such cases are handled by blocking the presupposition locally. - **Stated limitations:** asserted and presupposed information are not treated in a unified way, and defeasibility is not addressed. Both are deferred to follow-up work. ## Interesting ideas - Treating presupposition as information weaker than assertion, so it is dropped whenever it duplicates or contradicts an asserted literal, gives one principled filter instead of a separate projection rule for each connective. - Expanding disjunctions and conditionals into every compatible truth combination, not the minimal proof-oriented set, keeps all atoms visible on every alternative and makes "open possibilities" explicit. - Checking presuppositions locally per alternative, rather than globally against the whole context, is what lets the method handle mixed cases where some readings support a presupposition and others refute it. - Defining satisfaction and cancellation as "does adding ¬φ, or φ, make the state inconsistent" turns vague pragmatic notions into mechanical consistency tests. - Because the rules rely only on general semantics plus the Coverage Property, new connectives can be added without new presupposition rules. ## For Mova How these ideas could serve Mova, our small open language model — its files, stages and tests: - **I1** (frames): prag could store presupposition triggers (definites, factives) as weak candidate facts and discard them when the clause or the discourse already asserts or denies them. - **I2** (world): when a text says "either X or Y", the world model could keep fully enumerated alternative worlds, where X and Y each appear as true or false, and prune them as later sentences close some of them. - **I3** (answer): a QA reader on tales could check a question's presupposition (e.g. "Why did the fox leave?") branch by branch. It would answer "unknown" or point out a false premise when the alternatives disagree. - **I4** (learn): these closure tests could serve as negative controls in evaluation, checking that the system never asserts a presupposition the world state cancels. - **I5** (frames): new discourse connectives (e.g. *unless*, *only if*) could be supported just by giving their truth-table expansion, with presupposition handling inherited automatically. *Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.* ## Institutions - [Imperial College London](https://md.research.elamur.ai/free/en/universities/imperial-college-london/) — University, London, United Kingdom · 48 works · 12,181 citations 📚 Shelves (5): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 16,667 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 16,194 works · [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 16,039 works · [🗣️ Language and Linguistics](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/language-and-linguistics/) · 15,891 works · [🧮 Computational Theory and Mathematics](https://md.research.elamur.ai/free/en/shelves/computer-science/computational-theory-and-mathematics/) · 252 works 🧭 Topics (1): [😉 Implicature](https://md.research.elamur.ai/free/en/topics/implicature/) · 138 works ## Cite Cite as: Pablo Gervas. 1995. Compositionality for Presuppositions over Tableaux. arXiv:cmp-lg/9505014. The paper itself, not this page. BibTeX from the library's record of the work. ```bibtex @misc{gervas1995compositionality, title = {{Compositionality for Presuppositions over Tableaux}}, author = {Pablo Gervas}, year = {1995}, doi = {10.48550/arxiv.cmp-lg/9505014}, eprint = {cmp-lg/9505014}, archivePrefix = {arXiv}, url = {https://doi.org/10.48550/arxiv.cmp-lg/9505014} } ``` - [← previous A Uniform Treatment of Pragmatic Inferences in Simple and Complex Utterances and Sequences of Utterances](https://md.research.elamur.ai/free/en/papers/marcu-1995-uniform-treatment-pragmatic-inferences-simple/) - [next → Eurotra, history and results](https://md.research.elamur.ai/free/en/papers/maegaard-1995-eurotra-history-results/) - [↑ back to papers of 1995](https://md.research.elamur.ai/free/en/papers/1995/) ## References 12 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet. 1. Beaver, David, ‘The Kynematics of Presupposition’, in: H. Kamp (ed.), Presupposition, Dyana Report R2.2.A, Part II, Centre for Cognitive Science, University of Edimburgh, August 1993. [find](https://scholar.google.com/scholar?q=Beaver%2C+David%2C+%E2%80%98The+Kynematics+of+Presupposition%E2%80%99%2C+in%3A+H%2E+Kamp+%28ed%2E%29%2C+Presupposition%2C+Dyana+Report+R2%2E2%2EA%2C+Part+II%2C+Centre+for+Cognitive+Science%2C+University+of+Edimburgh%2C+August+1993%2E) 2. Beaver, David, What Comes First in Dynamic Semantics, Institute for Logic, Language and Computation, Amsterdam, 1993. [find](https://scholar.google.com/scholar?q=Beaver%2C+David%2C+What+Comes+First+in+Dynamic+Semantics%2C+Institute+for+Logic%2C+Language+and+Computation%2C+Amsterdam%2C+1993%2E) 3. Fitting, Melvin, First Order Logic and Automated Theorem Proving, Springer Verlag, New York, 1989. [find](https://scholar.google.com/scholar?q=Fitting%2C+Melvin%2C+First+Order+Logic+and+Automated+Theorem+Proving%2C+Springer+Verlag%2C+New+York%2C+1989%2E) 4. Gazdar, Gerald, Pragmatics, 1979. [find](https://scholar.google.com/scholar?q=Gazdar%2C+Gerald%2C+Pragmatics%2C+1979%2E) 5. Gazdar, Gerald, ‘A Solution to the Projection Problem’ in: Syntax and Semantics 11. Presupposition, 1979. [↗](https://doi.org/10.1163/9789004368880_003) 6. Heim, Irene, The Semantics of Definite and Indefinite Noun Phrases, PhD Thesis, University of Massachusetts, 1982. [find](https://scholar.google.com/scholar?q=Heim%2C+Irene%2C+The+Semantics+of+Definite+and+Indefinite+Noun+Phrases%2C+PhD+Thesis%2C+University+of+Massachusetts%2C+1982%2E) 7. Heim, Irene, ‘On the projection problem for presuppositions’, in: D. Flickinger et al (eds.), Proceedings of the Second West Coast Conference on Formal Linguistics, 1983. Reprinted in: S. Davis (ed.), Pragmatics, OUP, New York, 1991. [find](https://scholar.google.com/scholar?q=Heim%2C+Irene%2C+%E2%80%98On+the+projection+problem+for+presuppositions%E2%80%99%2C+in%3A+D%2E+Flickinger+et+al+%28eds%2E%29%2C+Proceedings+of+the+Second+West+Coast+Conference+on+Formal+Linguistics%2C+1983%2E+Reprinted+in%3A+S%2E+Davis+%28ed%2E%29%2C) 8. Karttunen, Lauri, ‘Presupposition of Compound Sentences’, Linguistic Inquiry, Volume IV, Number 2 (Spring 1973). [find](https://scholar.google.com/scholar?q=Karttunen%2C+Lauri%2C+%E2%80%98Presupposition+of+Compound+Sentences%E2%80%99%2C+Linguistic+Inquiry%2C+Volume+IV%2C+Number+2+%28Spring+1973%29%2E) 9. Karttunen, Lauri, ‘Presupposition and Linguistic Context’, Theoretical Linguistics I, 1974. [↗](https://doi.org/10.1515/thli.1974.1.1-3.181) 10. Karttunnen and Peters ‘Conventional Implicature’, in: Syntax and Semantics 11. Presupposition, 1979. [find](https://scholar.google.com/scholar?q=Karttunnen+and+Peters+%E2%80%98Conventional+Implicature%E2%80%99%2C+in%3A+Syntax+and+Semantics+11%2E+Presupposition%2C+1979%2E) 11. Mercer, Robert, ‘Towards a Common Logical Semantics for Presuppositions and Entailment’, Journal of Semantics, Volume 9, Number 3, 1992, pp 223-250. [find](https://scholar.google.com/scholar?q=Mercer%2C+Robert%2C+%E2%80%98Towards+a+Common+Logical+Semantics+for+Presuppositions+and+Entailment%E2%80%99%2C+Journal+of+Semantics%2C+Volume+9%2C+Number+3%2C+1992%2C+pp+223%2D250%2E) 12. Van der Sandt, Rob A., ‘Presupposition Projection as Anaphora Resolution’, Journal of Semantics, 9, 1992, pp333-377. Helm, London, 1988. [find](https://scholar.google.com/scholar?q=Van+der+Sandt%2C+Rob+A%2E%2C+%E2%80%98Presupposition+Projection+as+Anaphora+Resolution%E2%80%99%2C+Journal+of+Semantics%2C+9%2C+1992%2C+pp333%2D377%2E+Helm%2C+London%2C+1988%2E) *Updated 1 November 2026*