Ma191c Spring 2024: Mathematical Models of Generative Linguistics
Caltech, Linde Hall Room 289, Tuesday-Thursday 1:00-2:30pm
Instructor:
Matilde Marcolli
Brief Course Description
The goal of this class is to present a new mathematical model
of generative linguistics developed by Marcolli-Chomsky-Berwick
during the course of the past year. The class will include some
preliminary background on generative linguistics with main focus
on syntax.
Slides of Lectures
Slides of lectures will be posted here as the class progresses
First Part: Some General Linguistics Background and History of Generative Linguistics
- pdf What is linguistics?
- pdf Generative Linguistics
- pdf Mathematics of Formal Languages
- pdf Form formal languages to Minimalism
- pdf Probabilities in Computational Linguistics
- pdf Strong Minimalist Thesis
Second Part: Mathematical Structure of Syntactic Merge
- pdf Merge and Hopf algebras
- pdf Externalization
Summary of lectures
- Tuesday April 2: introduction to linguistics: phonology, morphology, syntax, semantics; generative linguistics and its history; recursions in language and the theory of formal languages, Chomsky hierarchy
- Thursday April 4: cross-serial recursions in Dutch and Swiss German, mildly context sensitive grammars; quick overview of transformational grammar, principles and parameters, government and binding, minimalist program, more detailed discussion of formal languages, proof of Chomsky hierarchy and machine recognition
- Tuesday April 9: continuation of proof of Chomsky hierarchy and machine recognition, formal languages and group theory; tree adjoining grammars (TAGs); more details on transformational grammar; multiple context free grammars (mCFGs)
- Thursday April 11: computational minimalism, merge and move, external and internal merge, feature checking, derivations, merge grammars (MGs) and mCFGs; entropy and Shannon information, N-grams, probabilities and CFGs, probabilities and TAGs, probabilistic versus deterministic systems
- Tuesday April 16: probabilities and CFGs, probabilities and TAGs, probabilistic versus deterministic systems; New Minimalism: Strong Minimalist Thesis, Merge, overview of the main elements of the theory; magma of syntactic objects, generative process of syntactic objects as combinatorial Dyson-Schwinger equation, workspaces as binary forests
- Thursday April 18: Hopf algebras, product and coproduct and relations, graded connected Hopf algebras and antipode, combinatorial Hopf algebras, commutative Hopf algebras and affine group schemes, Hopf algebra of workspaces, different forms of coproduct and relations, different algebraic properties
- Tuesday April 23: Merge operators on workspaces, forms of Merge, External and Internal Merge, Sideward Merge, Internal Merge and magma unit, Minimal Search and cost function, Minimal Yield constraints, no complexity loss constraint, n-ary Merge undergeneration and overgeneration
- Thursday April 25: Merge as a Hopf algebra Markov chain, countercyclic movement and Late Merge and the insertion Lie algebra, Milnor-Moore theorem, head functions, head function and planar embeddings (Kayne's LCA), head and complement, phase theory, phases algorithm, labeling algoritm, phases and block spin renormalization, FormSet, prelude to Externalization: the Dutch cross-serial example
- Tuesday April 30: Theta theory, theta roles, operads, colored operads, obligatory control, FormCopy, restriction to diagonals; Externalization as correspondences, language-dependent planarization section, projection by syntactic parameters
- Thursday May 2: syntactic parameters, available data (SSWL, LanGeLin), structure in data, dimensionality, evidence of relation (deviation from Markov evolution on phylogenetic trees and coding theory perspective), independent coordinates by Belkin-Niyogi Laplacian embedding, clusters of syntactic parameters
- Tuesday May 7:
- Thursday May 9:
- Tuesday May 14:
- Thursday May 16:
- Tuesday May 21:
- Thursday May 23:
- Tuesday May 28:
- Thursday May 30:
- Tuesday June 4: final presentations
- Thursday June 6: final presentations
Reading Materials
There is no specific textbook for the class, but the following references will be useful
Books
- Noam Chomsky et al. "Merge and the Strong Minimalist Thesis", Cambridge 2023, pdf
- Matilde Marcolli, Noam Chomsky, Robert Berwick "Mathematical Structure of Syntactic Merge", MIT Press to appear, pdf
Papers (more references will be added here shortly)
- Generative syntax
- pdf Howard Lasnik, Syntactic Structures Revisited
- New Minimalism
- pdf Noam Chomsky, UCLA Lectures, 2019
- pdf Noam Chomsky, Minimalism: where are we now and where we can hope to go? 2021
- pdf Noam Chomsky, Some puzzling foundational issues, 2019
- pdf Noam Chomsky, Problems of Projection, 2013
- pdf Noam Chomsky, On Phases, 2008
- pdf Riny Huijbregts, Empirical cases that rule out Ternary Merge, 2021
- Computational Minimalism
- pdf Chris Collins and Edward Stabler, A Formalization of Minimalist Syntax, 2017
- Hopf algebras
- pdf Pawel Blasiak, Combinatorial route to algebra: the art of composition and decomposition, 2010
- pdf Jean-Louis Loday, Maria Ronco, Combinatorial Hopf Algebras, 2008
- pdf
M.Aguilar, N.Bergeron, F.Sottile, Combinatorial Hopf algebras and
generalized Dehn-Sommerville relations, 2014
- pdf D.Calaque, K.Ebrahimi-Fard, D.Machon, Two interacting Hopf algebras of trees: A Hopf-algebraic approach to composition and substitution of B-series
- pdf Persi Diaconis, C. Y. Amy Pang, Arun Ram, Hopf algebras and Markov chains: Two examples and a theory
- pdf C. Y. Amy Pang, Markov Chains from Descent Operators on Combinatorial Hopf Algebras
- Syntactic Parameters
- pdf G.Longobardi, A.Treves, Grammatical Parameters from a Gene-like Code to Self-Organizing Attractors: a research program
- pdf Ian Roberts, Parameter hierarchies and Universal Grammar
- pdf G.Longobardi et al, Toward a syntactic phylogeny of modern Indo-European languages
- pdf S. Gakkhar, M. Marcolli, Syntactic Structures and the General Markov Models
- pdf A.Port, T.Karidi, M.Marcolli, Topological analysis of syntactic structures
- pdf A.Ortegaray, R.Berwick, M.Marcolli, Heat Kernel Analysis of Syntactic Structures
- pdf K.Shu, M.Marcolli, Syntactic structures and code parameters
- pdf J.Park et al, Prevalence and recoverability of syntactic parameters in sparse distributed memories
- pdf K.Shiva, J.Tao, M.Marcolli, Syntactic Parameters and Spin
Glass Models of Language Change
- pdf K.Shu, A.Ortegaray, R.Berwick, M.Marcolli, Phylogenetics of Indo-European Language Families via an
Algebro-Geometric Analysis of Their Syntactic Structures
Suggested readings for presentations
(more will be added shortly)
- Generative syntax
- pdf
Noam Chomsky, "Three models for the description of Language"
- pdf S.Ginsburg, B.Partee, Mathematical Model of Transformational Grammar
- Computational Minimalism
- pdf E.P.Stabler, "Computational perspectives on minimalism"
- pdf P.beim Graben, S.Gerth, "Geometric representations for minimalist grammars"
- pdf R.C.Berwick, "Mind the Gap"
- pdf T.Hunter, C.Dyer, "Distributions on Minimalist Grammar Derivations"
- Formal languages
- pdf N.Chomsky, M.Schutzenberger, The Algebraic Theory of Context-free Languages
- pdf P.A.Mellies, N.Zeilberger, Parsing as a lifting problem and the
Chomsky-Schutzenberger representation theorem
- pdf S.Giraudo, J.G.Luque, L.Mignot, F.Nicart, "Operads, quasiorders and regular languages"
- pdf L.Sennhauser, R.C.Berwick, "Evaluating the Ability of LSTMs to Learn Context-Free Grammars"
- pdf J.Shallit, "Number Theory and Formal Languages"
- pdf N.Ghani, A.Kurz, Higher dimensional trees algebraically
- syntactic parameters
- pdf R.Clark, "Kolmogorov complexity and the information content of parameters"
- pdf Partha Niyogi, Robert C. Berwick, "A dynamical systems model for language change"
Schedule of Final Presentations