Cyclic pregroups and natural language: a computational algebraic analysis (original) (raw)

M.: Clitic Movement in Pregroup Grammar: a Crosslinguistic Approach

2011

Abstract. The calculus of pregroups has been introduced by Lam-bek [10] as an algebraic (and logical) procedure for generating the gram-matical analysis of natural languages; it has been applied to a wide range of languages from English and German, to French and Italian, and many others [7]. Pregroups are non-commutative structures, but the syntax of natural languages shows the presence also of cyclic patterns, e.g. those caused by the the so called movements of clitic pronouns. In this paper we propose an extension of the calculus of pregroups including two cyclic meta-rules and use them to formally analyze movement of clitic clusters in Persian, French, and Italian. We also point out that these rules are inspired by Yetter’s and Abrsuci’s cyclic rules for Linear Logic.

A control language for transformational grammar

1968

Various orders of application of transformations have been considered in transformational grammar, ranging from unorder to cyclical orders involving notions of "lowest sentence" and of numerical indices on depth of embedding. The general theory of transformational grammar does not yet offer a uniform set of "traffic rules" which are accepted by most linguists. Thus, in designing a model of transformational grammar, it seems advisable to allow the specification of the order and point of application of transformations to be a proper part of the grammar. In this paper we present a simple control language designed to be used by linguists for this specification. In the control language the user has the ability to: 1. Group transformations into ordered sets and apply transformations either individually or by transformation set. 2. Specify the order in which the transformation sets are to be considered. 3. Specify the subtrees in which a transformation set is to be appl...

Formalization of Word-Order Shifts by Restarting Automata

2013

The phenomenon of word order freedom plays an important role in syntactic analysis of many natural lan- guages. This paper introduces a notion of a word order shift, an operation reflecting the degree of word order free- dom of natural languages. The word order shift is an op- eration based upon word order changes preserving syntac- tic correctness, individual word forms, their morphologi- cal characteristics, and their surface dependency relations in a course of a stepwise simplification of a sentence, a so called analysis by reduction. The paper provides linguistic motivation for this opera- tion and concentrates on a formal description of the whole mechanism through a special class of automata, so called restarting automata with the shift operation enhanced with a structured output, and their computations. The goal of this study is to clarify the properties of com- putations needed to perform (enhanced) analysis by reduc- tion for free word order languages.

Grammar Equations

arXiv (Cornell University), 2021

Diagrammatically speaking, grammatical calculi such as pregroups provide wires between words in order to elucidate their interactions, and this enables one to verify grammatical correctness of phrases and sentences. In this paper we also provide wirings within words. This will enable us to identify grammatical constructs that we expect to be either equal or closely related. Hence, our work paves the way for a new theory of grammar, that provides novel `grammatical truths'. We give a nogo-theorem for the fact that our wirings for words make no sense for preordered monoids, the form which grammatical calculi usually take. Instead, they require diagrams -- or equivalently, (free) monoidal categories.