General Information
| Instructor(s) | Pascal Amsili, Angelo Ortiz Tandazo (TA) |
| Place, time |
Wednesdays, 14:00-16:00 (CM); Fridays, 16:00-18:00 (TA sessions). ENS 29 rue d'Ulm, room Ribot Starting February 4. |
| Credits | 6 ECTS |
| Content (English) | This course aims to introduce a range of formal and computational tools relevant to contemporary research in linguistics (and beyond). For the first time this year, we begin with two major advances in artificial intelligence for language processing: lexical embeddings and large language models. These will be presented in terms of their core principles and their utility for research in linguistics, psycholinguistics, and cognitive science. The remainder of the course will focus on formal frameworks—primarily from discrete mathematics—developed in the 20th century, which enable precise and rigorous manipulation of syntax (formal languages, grammars, automata), semantics (first-order logic), and the interface between the two (lambda calculus). These tools ultimately support the research program initiated by Montague: treating English as a formal language. |
| Content (French) | L'objet de cet enseignement est d'introduire une palette d'outils formels ou computationnels pertinents pour la recherche contemporaine en linguistique (et au delà). Pour la première fois cette année, on commence par deux avancées majeures dans le domaine du traitement de la langue par l'intelligence artificielle, d'une part les plongements lexicaux (lexical embeddings), d'autre part les grands modèles de langue qui seront présentés dans leurs grands principes et du point de vue de leur utilité pour la recherche en linguistique, psycholinguistique et sciences cognitives. La suite du cours portera sur des cadres formels (principalement de mathématiques discrètes) élaborés au XXe siècle et permettant de manipuler de façon précise et rigoureuse la syntaxe (langages formels, grammaires, automates), la sémantique (logique du premier ordre), et la relation entre les deux (lambda-calcul), jusqu'à offrir les outils pour mener le programme de recherche initié par Montague: le traitement de l'anglais comme un langage formel. |
| Course taught in | English |
| Teaching format | On-site teaching. Students who need to follow the class off-site should contact the instructor asap. |
| Links | Schedule ; Moodle ; Master de Sciences Cognitives (ancien CogMaster). https://master-cognitive-science.ens.psl.eu/en/formal-tools-study-language-pascal-amsili-18009 |
| Previous classes |
Web page of last year's class: 2024/25
This very class was previously taught with a different format (3 hours per week), with a slightly different audience (students from the CogMaster), at a different stage of the curriculum. Yet the following pages offer resources that may be relevant (slides, previous exams, exercices with answers, etc.): 2023/24 ; 2022/23 ; 2021/22 ; 2020/21 ; 2019/20. |
Assessments
| Mode of assesment | There will be three homework assignments (worth 60% of the final grade) and a final exam (worth 40%
of the final grade). Homeworks can be handed in in class (paper) or on moodle (pdf format). On moodle the deadline is 23:59. |
| Homework #1 (03-25) | tba (due April, 15) |
| Homework #2 (04-15) | tba (due May, 6) |
| Homework #3 (05-13) | tba (due June, 3) |
| Results | tba |
Schedule (tentative)
| wk. | date | type | description | links |
|---|---|---|---|---|
| 1 | 2026-02-04 | CM (pa) | Distributional Semantics and Language Models (DSLM) : Lexical semantics | overview; slides: Lexical relations |
| 2026-02-06 | TD (pa) | DSLM 2: The distributional hypothesis | ||
| 2 | 2026-02-11 | CM (pa) | DSLM 3: The distributional hypothesis (cont'd) | Slides used in class: Term-term matrices |
| 2026-02-13 | TP (pa) | DSLM 4: Static word embeddings | overview (completed); | |
| 3 | 2026-02-18 | CM (pa) | DSLM 5: Large Language Models |
overview
Slides (in French) about the perceptron: local version, in line version. |
| 2026-02-20 | TD (pa) | DSLM 6: LLMs (cont'd) | Slides: Jurafsky & Martin's chapter 7 | |
| - | 2026-02-25 | CM | No class (academic break) | |
| 2026-02-27 | TD | |||
| - | 2026-03-04 | CM | No class (PSL Week) | |
| 2026-03-06 | TD | |||
| 4 | 2026-03-11 | CM (pa) | DSLM 7: LLM (end) Formal Language Theory (FLT): Formal Languages |
Slides: Issues with LLMs ;
Formal Language Theory |
| 2026-03-13 | TD (aot) | Regular languages (Automata) | ||
| 5 | 2026-03-18 | CM (aot) | FLT 2: Regular languages | |
| 2026-03-20 | TD (aot) | Automata, regular expressions, regular grammars | ||
| 6 | 2026-03-25 | CM (aot) | FLT 3: Formal Grammars and complexity | |
| 2026-03-27 | TD (aot) | Formal grammars | ||
| 7 | 2026-04-01 | CM (pa) | FLT 4: Complexity of Natural Language(s) | |
| 2026-04-03 | TD (aot) | Formal grammars | ||
| 8 | 2026-04-08 | CM (pa) | First Order Logic (FOL): Crash course in propositional logic | |
| 2026-04-10 | TD (aot) | Propositional logic | ||
| 9 | 2026-04-15 | CM (aot) | FOL 2: Crash course in predicate logic | |
| 2026-04-17 | TD (aot) | Predicate logic | ||
| 10 | 2026-04-22 | CM (pa) | FOL 3: Quantification in Natural Language | |
| 2026-04-19 | TD (aot) | Predicate Logic | ||
| - | 2026-04-22 | CM | No class (academic break) | |
| 2026-04-25 | TD | |||
| 11 | 2026-05-06 | CM (pa) | Compositionality and λ-calculus (CLC) : Typed λ-calculus | |
| - | 2026-05-08 | TD | No class | |
| 12 | 2026-05-13 | CM (pa) | CLC 2: Generalized Quantifiers | |
| - | 2026-05-15 | TD | No class | |
| 13 | 2026-05-20 | CM (pa) | CLC 3: English as a formal language | |
| 11 | 2026-05-22 | TD (aot) | First fragment | |
| - | 2026-05-25 | CM | No class | |
| 12 | 2026-05-27 | TD (aot) | Fragment | |
| - | 2026-06-03 | CM | No class | |
| 13 | 2026-06-05 | TD (aot) | Exam (2h) | |
Pointers (references, bibliography, online resources)
- A nice video about Turing Machines (in French)
- About First Order Logic, a 28p. hand-out (in French) that may be useful.
- About regular languages and automata, a 30p. hand-out (in French) that may be useful (covers additional material and algorithms).
- Barbara Partee, Alice ter Meulen & Robert E. Wall, Mathematical Methods in Linguistics, Kluwer Academic Publishers, 1993.
- Gamut, L. T. F. (1991). Logic, Language, and Meaning, volume 1: Introduction to Logic; volume 2: Intensional Logic and Logical Grammar. University of Chicago Press.
- About the complexity of natural language, a relatively recent survey can be found here: António Branco, 2018: Computational Complexity of Natural Languages: A Reasoned Overview.
- For those interested in pure untyped lambda-calculus : The Interactive Lambda-calculus Tracer: TILC aims to be a friendly visual tool for teaching/studying main basic pure untyped lambda-calculus concepts.
- More directly relevant to the fragment construction process we've been practicing: the lambda-calculator (formerly the Penn Lambda Calculator).
- More about λ-calculus: very useful lecture notes from this class:
CS 152, Programming Languages (Harvard, 2016):
- Pure language,
- Combinators,
- Typed language (the last one is less relevant for us).
- A recent book about computability and complexity was recently published at MIT Press (author Hubie Chen), and the first part, which is published under a creative commons licence, is a very precise and complete chapter on automata theory. Available HERE.
