Unbounded Recursion in Two Dimensions, Where Syntax and Prosody Meet

Both syntax and prosody seem to require structures with unbounded branching, something that is not immediately provided by multiple context free grammars or other equivalently expressive formalisms. That extension is easy, and does not disrupt an appealing model of prosody/syntax interaction. Rather than computing prosodic and syntactic structures independently and then selecting optimally corresponding pairs, prosodic structures can be computed directly from the syntax, eliminating alignment issues and the need for bracket-insertion or other ad hoc devices. To illustrate, a simple model of prosodically-defined Irish pronoun displacement is briefly compared to previous proposals

A Case Study of the Convergence of Mildly Context-Sensitive Formalisms for Natural Language Syntax: from Minimalist Grammars to Multiple Context-Free Grammars

Soumis en tant que rapport de recherche INRIA Futurs - Projet SIGNESThe present work is set in the field of natural language syntactic parsing. We present the concept of "mildly context-sensitive" grammar formalisms, which are full-fetched and efficient for syntactic parsing. We summarize a number of these formalisms' definitions, together with the relations between one another, and, most importantly, a survey of known equivalences. The conversion of Edward Stabler's Minimalist Grammars into Multiple Context-Free Grammars (MCFG) is presented in particular detail, along with a study of the complexity of this procedure and of its implications for parsing. This report is an adaptation of the French Master thesis that bears the same name, from Bordeaux 1 University, June 2006

Categorial Minimalist Grammar: From Generative Syntax To Logical Form

International audienceWe first recall some basic notions on minimalist grammars and on categorial grammars. Next we shortly introduce partially commutative linear logic, and our representation of minimalist grammars within this categorial system, the so-called categorial minimalist grammars. Thereafter we briefly present λμ-DRT (Discourse Representation Theory) an extension of λ-DRT (compositional DRT) in the framework of λμ calculus: it avoids type raising and derives different readings from a single semantic representation, in a setting which follows discourse structure. We run a complete example which illustrates the various structures and rules that are needed to derive a semantic representation from the categorial view of a transformational syntactic analysis

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.Comment: 27 pages, LaTeX, 3 figure

Minimalist Grammars in the Light of Logic

In this paper, we aim at understanding the derivations of minimalist grammars without the shortest move constraint. This leads us to study the relationship of those derivations with logic. In particular we show that the membership problem of minimalist grammars without the shortest move constraint is as difficult as provability in Multiplicative Exponential Linear Logic. As a byproduct, this result gives us a new representation of those derivations with linear $\lambda$-terms. We show how to interpret those terms in a homomorphic way so as to recover the sentence they analyse. As the homorphisms we describe are rather evolved, we turn to a proof-net representation and explain how Monadic Second Order Logic and related techniques allow us both to define those proof-nets and to retrieve the sentence they analyse

Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546