8 papers
Merge on workspaces as Hopf algebra Markov chain
Matilde Marcolli, David Skigin
We study the dynamical properties of a Hopf algebra Markov chain with state space the binary rooted forests with labelled leaves. This Markovian dynamical system describes the core…
Extension Condition "violations" and Merge optimality constraints
Matilde Marcolli, Richard Larson, Riny Huijbregts
We analyze, using the mathematical formulation of Merge within the Strong Minimalist Thesis framework, a set of linguistic phenomena, including head-to-head movement, phrasal affix…
Hypermagmas and Colored Operads: Heads, Phases, and Theta Roles
Matilde Marcolli, Riny Huijbregts, Richard K. Larson
We show that head functions on syntactic objects extend the magma structure to a hypermagma, with the c-command relation compatible with the magma operation and the m-command relat…
A Lie-algebraic perspective on Tree-Adjoining Grammars
Isabella Senturia, Elizabeth Xiao, Matilde Marcolli
We provide a novel mathematical implementation of tree-adjoining grammars using two combinatorial definitions of graphs. With this lens, we demonstrate that the adjoining operation…
Encoding syntactic objects and Merge operations in function spaces
Matilde Marcolli, Robert C. Berwick
We provide a mathematical argument showing that, given a representation of lexical items as functions (wavelets, for instance) in some function space, it is possible to construct a…
The Algebraic Structure of Morphosyntax
Isabella Senturia, Matilde Marcolli
Within the context of the mathematical formulation of Merge and the Strong Minimalist Thesis, we present a mathematical model of the morphology-syntax interface. In this setting, m…