A game theoretical approach to the algebraic counterpart of the Wagner hierarchy

La hiérarchie de Wagner constitue à ce jour la plus fine classification des langages ω-réguliers. Par ailleurs, l'approche algébrique de la théorie de langages formels montre que ces ensembles ω-réguliers correspondent précisément aux langages reconnaissables par des ω-semigroupes finis pointés. Ce travail s'inscrit dans ce contexte en fournissant une description complète de la contrepartie algébrique de la hiérarchie de Wagner, et ce par le biais de la théorie descriptive des jeux de Wadge. Plus précisément, nous montrons d'abord que le degré de Wagner d'un langage ω-régulier est effectivement un invariant syntaxique. Nous définissons ensuite une relation de réduction entre ω-semigroupes pointés par le biais d'un jeu infini de type Wadge. La collection de ces structures algébriques ordonnée par cette relation apparaît alors comme étant isomorphe à la hiérarchie de Wagner, soit un quasi bon ordre décidable de largeur 2 et de hauteur ω. Nous exposons par la suite une procédure de décidabilité de cette hiérarchie algébrique : on décrit une représentation graphique des ω-semigroupes finis pointés, puis un algorithme sur ces structures graphiques qui calcule le degré de Wagner de n'importe quel élément. Ainsi le degré de Wagner de tout langage ω-régulier peut être calculé de manière effective directement sur son image syntaxique. Nous montrons ensuite comment construire directement et inductivement une structure de n''importe quel degré. Nous terminons par une description détaillée des invariants algébriques qui caractérisent tous les degrés de cette hiérarchie. Abstract The Wagner hierarchy is known so far to be the most refined topological classification of ω-rational languages. Also, the algebraic study of formal languages shows that these ω-rational sets correspond precisely to the languages recognizable by finite pointed ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation on finite pointed ω-semigroups by means of a Wadge-like infinite two-player game. The collection of these algebraic structures ordered by this reduction is then proven to be isomorphic to the Wagner hierarchy, namely a well-founded and decidable partial ordering of width 2 and height $\omega^\omega$. We also describe a decidability procedure of this hierarchy: we introduce a graph representation of finite pointed ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of every ω-rational language can therefore be computed directly on its syntactic image. We then show how to build a finite pointed ω-semigroup of any given Wagner degree. We finally describe the algebraic invariants characterizing every Wagner degree of this hierarchy.

Complex syntax in autism spectrum disorders: a study of relative clauses.

BACKGROUND: The few studies that have evaluated syntax in autism spectrum disorder (ASD) have yielded conflicting findings: some suggest that once matched on mental age, ASD and typically developing controls do not differ for grammar, while others report that morphosyntactic deficits are independent of cognitive skills in ASD. There is a need for a better understanding of syntax in ASD and its relation to, or dissociation from, nonverbal abilities. AIMS: Syntax in ASD was assessed by evaluating subject and object relative clause comprehension in adolescents and adults diagnosed with ASD with a performance IQ within the normal range, and with or without a history of language delay. METHODS & PROCEDURES: Twenty-eight participants with ASD (mean age 21.8) and 28 age-matched controls (mean age 22.07) were required to point to a character designated by relative clauses that varied in syntactic complexity. OUTCOMES & RESULTS: Scores indicate that participants with ASD regardless of the language development history perform significantly worse than age-matched controls with object relative clauses. In addition, participants with ASD with a history of language delay (diagnosed with high-functioning autism in the DSM-IV-TR) perform worse on subject relatives than ASD participants without language delay (diagnosed with Asperger syndrome in the DSM-IV-TR), suggesting that these two groups do not have equivalent linguistic abilities. Performance IQ has a positive impact on the success of the task for the population with ASD. CONCLUSIONS & IMPLICATIONS: This study reveals subtle grammatical difficulties remaining in adult individuals with ASD within normal IQ range as compared with age-matched peers. Even in the absence of a history of language delay in childhood, the results suggest that a slight deficit may nevertheless be present and go undetected by standardized language assessments. Both groups with and without language delay have a similar global performance on relative clause comprehension; however, the study also indicates that the participants with reported language delay show more difficulty with subject relatives than the participants without language delay, suggesting the presence of differences in linguistic abilities between these subgroups of ASD.

Contrast : a concept in language and its development in Medieval Spanish

The purpose of this PhD thesis is to investigate a semantic relation present in the connection of sentences (more specifically: propositional units). This relation, which we refer to as contrast, includes the traditional categories of adversatives - predominantly represented by the connector but in English and pero in Modern Spanish - and concessives, prototypically verbalised through although / aunque. The aim is to describe, analyse and - as far as possible - to explain the emergence and evolution of different syntactic schemes marking contrast during the first three centuries of Spanish (also referred to as Castilian) as a literary language, i.e., from the 13th to the 15th century. The starting point of this question is a commonplace in syntax, whereby the semantic and syntactic complexity of clause linkage correlates with the degree of textual elaboration. In historical linguistics, i.e., applied to the phylogeny of a language, it is commonly referred to as the parataxis hypothesis A crucial part of the thesis is dedicated by the definition of contrast as a semantic relation. Although the label contrast has been used in this sense, mainly in functional grammar and text linguistics, mainstream grammaticography and linguistics remain attached to the traditional categories adversatives and concessives. In opposition to this traditional view, we present our own model of contrast, based on a pragma-semantic description proposed for the analysis of adversatives by Oswald Ducrot and subsequently adopted by Ekkehard König for the analysis of concessives. We refine and further develop this model in order for it to accommodate all, not just the prototypical instances of contrast in Spanish, arguing that the relationship between adversatives and concessives is a marked opposition, i.e., that the higher degree of semantic and syntactic integration of concessives restricts some possible readings that the adversatives may have, but that this difference is almost systematically neutralised by contextual factors, thus justifying the assumption of contrast as a comprehensive onomasiological category. This theoretical focus is completed by a state-of-the-question overview attempting to account for all relevant forms in which contrast is expressed in Medieval Spanish, with the aid of lexicographic and grammaticographical sources, and an empirical study investigating the expression of corpus in a corpus study on the textual functions of contrast in nine Medieval Spanish texts: Cantar de Mio Cid, Libro de Alexandre, Milagros de Nuestra Sehora, Estoria de Espana, Primera Partida, Lapidario, Libro de buen amor, Conde Lucanor, and Corbacho. This corpus is analysed using quantitative and qualitative tools, and the study is accompanied by a series of methodological remarks on how to investigate a pragma-semantic category in historical linguistics. The corpus study shows that the parataxis hypothesis fails to prove from a statistical viewpoint, although a qualitative analysis shows that the use of subordination does increase over time in some particular contexts.