Old and New Minimalism: a Hopf algebra comparison
In this paper we compare some old formulations of Minimalism, in particular Stabler's computational minimalism, and Chomsky's new formulation of Merge and Minimalism, from the point of view of their mathematical description in terms of Hopf algebras. We show that the newer formulation has a clear advantage purely in terms of the underlying mathematical structure. More precisely, in the case of Stabler's computational minimalism, External Merge can be described in terms of a partially defined operated algebra with binary operation, while Internal Merge determines a system of right-ideal coideals of the Loday-Ronco Hopf algebra and corresponding right-module coalgebra quotients. This mathematical structure shows that Internal and External Merge have significantly different roles in the old formulations of Minimalism, and they are more difficult to reconcile as facets of a single algebraic operation, as desirable linguistically. On the other hand, we show that the newer formulation of Minimalism naturally carries a Hopf algebra structure where Internal and External Merge directly arise from the same operation. We also compare, at the level of algebraic properties, the externalization model of the new Minimalism with proposals for assignments of planar embeddings based on heads of trees.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Syntax-semantics interface: an algebraic model
We extend our formulation of Merge and Minimalism in terms of Hopf algebras to an algebraic model of a syntactic-semantic interface. We show that methods adopted in the formulation of renormalization (extraction of meani…
modelMerge on workspaces as Hopf algebra Markov chain
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 computational process of structure form…
Digital (co)homology modules and digital Pontryagin algebras
In the current study, we explore digital homology and cohomology modules, and investigate their fundamental properties on pointed digital images. We also examine pointed digital Hopf spaces and base point preserving digi…
Coinductive guide to inductive transformer heads
We argue that all building blocks of transformer models can be expressed with a single concept: combinatorial Hopf algebra. Transformer learning emerges as a result of the subtle interplay between the algebraic and coalg…
A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks
In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state,…