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