Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure

Evaluating Structural Economy Claims in Relative Clause Attachment

Grillo and Costa (2014) argue for a pseudo- relative (PR) first account of relative clause attachment preferences (RC) such that, when faced with a sentence ambiguous between a PR and a RC interpretation, the parser prefers committing to a PR structure first, thus giving rise to what looks like a high-attachment preference. One possible explanation for this parsing choice is in terms of simplicity of the PR structure, and overall economy principles. Here, we evaluate this hypothesis by testing the predictions of a parser for Minimalist grammars for PR and RC structures in Italian. We discuss the relevance of our results for PR-first explanations of the cross-linguistic variability of RC attachment biases, and highlight the role that computational models can play in evaluating the cognitive plausibility of economy considerations tied to fine-grained structural analyses

Grammar Size and Quantitative Restrictions on Movement

Recently is has been proved that every Minimalist grammar can be converted into a strongly equivalent single movement normal form such that every phrase moves at most once in every derivation. The normal form conversion greatly simplifies the formalism and reduces the complexity of movement dependencies, but it also runs the risk of greatly increasing the size of the grammar. I show that no such blow-up obtains with linguistically plausible grammars that respect common constraints on movement. This establishes not only the cost-free nature of this normal form for realistic grammars, but also that the known restrictions on movement greatly reduce the range of licit movement configurations relative to what unconstrained Minimalist grammars are capable of. Moreover, this work constitutes a first step towards a quantitatively grounded view of movement

C-Command Dependencies as TSL String Constraints

We provide a general framework for analyzing c-command based dependencies in syntax, e.g. binding and NPI licensing, from a subregular perspective. C-command relations are represented as strings computed from Minimalist derivation trees, and syntactic dependencies are shown to be input-output tier-based strictly local over such strings. The complexity of many syntactic phenomena thus is comparable to dependencies in phonology and morphology

Evolution, Perfection, and Theories of Language

In this article it is argued that evolutionary plausibility must be made an important constraining factor when building theories of language. Recent suggestions that presume that language is necessarily a perfect or optimal system are at odds with this position, evolutionary theory showing us that evolution is a meliorizing agent often producing imperfect solutions. Perfection of the linguistic system is something that must be demonstrated, rather than presumed. Empirically, examples of imperfection are found not only in nature and in human cognition, but also in language — in the form of ambiguity, redundancy, irregularity, movement, locality conditions, and extra-grammatical idioms. Here it is argued that language is neither perfect nor optimal, and shown how theories of language which place these proper-ties at their core run into both conceptual and empirical problems

Viable Syntax: Rethinking Minimalist Architecture

Hauser et al. (2002) suggest that the human language faculty emerged as a genetic innovation in the form of what is called here a ‘keystone factor’—a single, simple, formal mental capability that, interacting with the pre-existing faculties of hominid ancestors, caused a cascade of effects resulting in the language faculty in modern humans. They take Merge to be the keystone factor, but instead it is posited here that Merge is the pre-existing mechanism of thought made viable by a principle that permits relations interpretable at the interfaces to be mapped onto c-command. The simplified minimalist architecture proposed here respects the keystone factor as closely as possible, but is justified on the basis of linguistic analyses it makes available, including a relativized intervention theory applicable across Case, scope, agreement, selection and linearization, a derivation of the A/A’-distinction from Case theory, and predictions such as why in situ wh-interpretation is island-insensitive, but susceptible to intervention effects

Case assignment in TSL syntax: a case study

Recent work suggests that the subregular complexity of syntax might be comparable to that of phonology and morphology. More specifically, whereas phonological and morphological dependencies are tier-based strictly local over strings, syntactic dependencies are tier-based strictly local over derivation trees. However, a broader range of empirical phenomena must be considered in order to solidify this claim. This paper investigates various phenomena related to morphological case, and we argue that they, too, are tier-based strictly local. Not only do our findings provide empirical support for a kind of computational parallelism across language modules, they also offer a new, computationally unified perspective of structural and lexical case. We hope that this paper will enable other researchers to fruitfully study syntactic phenomena from a subregular perspective

Curbing Feature Coding: Strictly Local Feature Assignment

Graf (2017) warns that every syntactic formalism faces a severe overgeneration problem because of the hidden power of subcategorization. Any constraint definable in monadic second-order logic can be compiled into the category system so that it is indirectly enforced as part of subcategorization. Not only does this kind of feature coding deprive syntactic proposals of their empirical bite, it also undermines computational efforts to limit syntactic formalisms via subregular complexity. This paper presents a subregular solution to feature coding. Instead of features being a cheap resource that comes for free, features must be assigned by a transduction. In particular, category features must be assigned by an input strictly local (ISL) tree-to-tree transduction, defined here for the first time. The restriction to ISL transductions correctly rules out various deviant category systems