Algebraic dependency grammar
- Autores: Carles Cardó
- Directores de la Tesis: Glyn Morrill (dir. tes.), José Oriol Valentin-Fernández Gallart (dir. tes.)
- Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2018
- Idioma: español
- Tribunal Calificador de la Tesis: Annie Foret (presid.), Mehrnoosh Sadrzadeh (secret.), Marco Kuhlmann (voc.)
- Programa de doctorado: Programa de Doctorado en Computación por la Universidad Politécnica de Catalunya
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- Resumen
We propose a mathematical formalism called Algebraic Dependency Grammar with applications to formal linguistics and to formal language theory. Regarding formal linguistics we aim to address the problem of grammaticality with special attention to cross-linguistic cases. In the field of formal language theory this formalism provides a new perspective allowing an algebraic classification of languages. Notably our approach suggests the existence of so-called anti-classes of languages associated to certain classes of languages.
Our notion of a dependency grammar is as of a definition of a set of well-constructed dependency trees (we call this algebraic governance) and a relation which associates word-orders to dependency trees (we call this algebraic linearization).
In relation to algebraic governance, we define a manifold which is a set of dependency trees satisfying an agreement condition throughout a pattern, which is the algebraic form of a collection of syntactic addresses over the dependency tree. A boolean condition on the words formalizes the notion of agreement.
In relation to algebraic linearization, first we observe that the notion of projectivity is quintessentially that certain substructures of a dependency tree always form an interval in its linearization. So we have to establish well what is a substructure; we see again that patterns proportion the key, generalizing the notion of projectivity with recursive linearization procedures.
Combining the above modules we have the formalism: an algebraic dependency grammar is a manifold together with a linearization.
Notice that patterns sustain both manifolds and linearizations. We study their interrelation in terms of a new algebraic classification of classes of languages.
We highlight the main contributions of the thesis. Regarding mathematical linguistics, algebraic dependency grammar considers trees and word-order different modules in the architecture, which allows description of languages with varied word-order. Ellipses are permitted; this issue is usually avoided because it makes some formalisms non-decidable.
We differentiate linguistic phenomena structurally by their algebraic description. Algebraic dependency grammar permits observance of affinity between linguistic constructions which seem superficially different.
Regarding formal language theory, a new system for understanding a very large family of languages is presented which permits observation of languages in broader contexts. We identify a new class named anti-context-free languages containing constructions structurally symmetric to context-free languages. Informally we could say that context-free languages are well-parenthesized, while anti-context-free languages are cross-serial-parenthesized. For example copy languages and respectively languages are anti-context-free.
