Grammaire | EPFL Graph Search

La grammaire est l'étude objective et systématique des éléments (phonème, morphème et mot) et des mécanismes et processus de formation, de construction et d'expression constitutifs d'une langue naturelle, écrite ou parlée, en particulier par l'étude de la morphologie et de la syntaxe et à l'exclusion de la phonologie, de la lexicologie, de la sémantique et de la stylistique. Par extension, on nomme aussi grammaire un manuel ou un ensemble de documents décrivant des règles grammaticales. Grammaire prescriptive (normative) et descriptive La grammaire étudie les règles qui régissent une langue donnée et permettent de construire des énoncés reconnus corrects par les locuteurs natifs de cette langue. La grammaire descriptive décrit comment la langue est, sans y porter jugement. La grammaire normative, donc prescriptive, juge un énoncé comme correct ou incorrect selon un standard. La grammaire normative est enseignée à l'école primaire et secondaire. Le terme « école de gram

Grammar-Based Tree Compression

Grammar-based compression means to find a small grammar that generates a given object. Such a grammar reveals the structure of the object (according to the grammar formalism used); the main advantage of this compression method is that the resulting grammar can often be used in further computations without prior decompression. A linear time bottom-up algorithm is presented which transforms a tree into a particular context-free tree grammar. For common XML documents the algorithm performs well, compressing the tree structure to about 5 per cent of the original size. The validation of an XML document against an XML type can be done without decompression, in linear time w.r.t. the size of the grammar (for a fixed type). While the involved grammars can be double exponentially smaller than the represented trees, testing them for equivalence can be done in polynomial space w.r.t. the sum of their sizes.

2004

The Learnability of the Grammar of Jazz: Bayesian Inference of Hierarchical Structures in Harmony

Daniel Harasim

Musical grammar describes a set of principles that are used to understand and interpret the structure of a piece according to a musical style. The main topic of this study is grammar induction for harmony --- the process of learning structural principles from the observation of chord sequences. The question how grammars are learnable by induction from sequential data is an instance of the more general question how abstract knowledge is inducible from the observation of data --- a central question of cognitive science. Under the assumption that human learning approximately follows the principles of rational reasoning, Bayesian models of cognition can be used to simulate learning processes. This study investigates what prior knowledge makes it possible to learn musical grammar inductively from Jazz chord sequences using Bayesian models and computational simulations. The theoretical part of the thesis presents how questions about learnability can be studied in a unified framework involving music analysis, cognitive modeling, Bayesian statistics, and computational simulations. A new grammar formalism, called Probabilistic Abstract Context-Free Grammar (PACFG), is proposed that allows for flexible probability models which facilitate the grammar-induction experiments of this study. PACFG can jointly model multiple musical dimensions such as harmony and rhythm, and can use coordinate ascent variational inference for grammar learning. The empirical part of the thesis reports supervised and unsupervised grammar-learning experiments. To train and evaluate grammar models, a ground-truth dataset of hierarchical analyses of complete Jazz standards, called the Jazz Harmony Treebank (JHT), was created. The supervised grammar-learning experiments, in which grammars for Jazz harmony are learned from the JHT analyses, show that jointly modeling harmony and rhythm significantly improves the grammar models' prediction of the ground truth. The performance and robustness of the grammars are further improved by a transpositionally invariant parameterization of rule probabilities. Following the supervised grammar learning, unsupervised grammar learning was performed by inducing harmony grammars merely from Jazz chord sequences, without the observation of the JHT trees. The results show that the best induced grammar performs similarly well as the best supervised grammar. In particular, the goal-directedness of functional harmony does not need to be assumed a priori, but can be learned without usage of music-specific prior knowledge. The findings of this thesis show that general prior knowledge enables an ideal learner to acquire abstract musical principles by statistical learning. In conclusion, it is plausible that much aspects of musical grammar have been learned by Jazz musicians and listeners, instead of being innate predispositions or explicitly taught concepts. This thesis is moreover embedded into the context of empirical music research and digital humanities. Current studies either describe complex musical structures qualitatively or investigate simpler aspects quantitatively. The computational models developed in this thesis demonstrate that deep insights into music and statistical analyses are not mutually exclusive. They enable a new kind of data-driven music theory and musicology, for instance through comparative analyses of musical grammar for different styles such as Jazz, Rock, and Western classical music.

EPFL2020

Harmonic Syntax in Time: Rhythm Improves Grammatical Models of Harmony

Daniel Harasim, Martin Alois Rohrmeier

Music is hierarchically structured, both in how it is perceived by listeners and how it is composed. Such structure can be elegantly captured using probabilistic grammatical models similar to those used to study natural language. They address the complexity of the structure using abstract categories in a recursive formalism. Most existing grammatical models of musical structure focus on one single dimension of music–such as melody, harmony, or rhythm. While these grammar models often work well on short musical excerpts, accurate analysis of longer pieces requires taking into account the constraints from multiple domains of structure. The present paper proposes abstract product grammars–a formalism which integrates multiple dimensions of musical structure into a single grammatical model–along with efficient parsing and inference algorithms for this formalism. We use this model to study the combination of hierarchically-structured harmonic syntax and hierarchically-structured rhythmic information. The latter is modeled by a novel grammar of rhythm that is capable of expressing temporal regularities in musical phrases. It integrates grouping structure and meter. The combined model of harmony and rhythm outperforms both single-dimension models in computational experiments. All models are trained and evaluated on a treebank of hand-annotated Jazz standards.

ISMIR2019

The Learnability of the Grammar of Jazz: Bayesian Inference of Hierarchical Structures in Harmony

Daniel Harasim

EPFL2020