L’objet de notre étude porte sur la logique et le langage à la transition entre le lycée et l’université dans le contexte camerounais. Au Cameroun, dans l’enseignement secondaire, les concepts de logique sont très peu explicités en classe de mathématiques, du fait que leur enseignement n’est pas prescrit par les nouveaux programmes1 officiels. Ce n’est pas le cas de l’enseignement supérieur où un cours de logique formelle sous forme de rappel, est souvent donné en début d’année. Ce cours n’est pas prescrit par les programmes, mais certains enseignants en voient la nécessité. Les résultats de plusieurs travaux ont montré que certaines des difficultés que les étudiants rencontrent dans la pratique des mathématiques proviennent d’une mauvaise maîtrise des concepts de logique. Nous faisons l’hypothèse qu’ils sont insuffisamment pris en charge pa rles enseignants dans la classe de mathématiques, qui pensent qu’ils sont disponibles chez les étudiants, du fait de leur utilisation dans la vie courante d’une part, et progressivement dans l’activité mathématique. La thèse que nous soutenons est que, pour rendre opératoire les concepts de logique chez lesétudiants nouvellement arrivés à l’université, un minimum d’explicitation de ces concepts en relation avec leur usage dans l’activité mathématique est nécessaire pour les apprentissages en mathématiques à tout le moins dans l’enseignement supérieur. Pour défendre notre thèse, nous avons divisé notre travail en deux parties. Dans la première partie, nous présentons des éléments théoriques et analytiques nécessaires à notre travail, et une revue des travaux antérieurs en relation avec notre problématique. La deuxième partie porte sur les résultats d’une expérimentation que nous avons menée avec des élèves de terminale C d’un lycée de Yaoundé 2, et des étudiants de première année de licence de mathématiques de l’Ecole Normale Supérieure de Yaoundé. Elle s’est déroulée en deux temps : nous avons fait passer un questionnaire portant sur la logique et le langage aux élèves et aux étudiants, et à la suite de ce questionnaire, nous avons organisé un module de suivi avec huit étudiants ayant passé ce questionnaire. Le questionnaire nous a permis de repérer certaines conceptions des élèves et des étudiants concernant les concepts de logique,et le module de suivi a permis de provoquer des débats qui permettaient dans certains cas d’affiner nos analyses et nous donnaient des éléments permettant d’identifier des occasions pour expliciter certaines notions. / Our study focuses on logic and language at the transition between high school and university in the Cameroonian context. In Cameroon secondary education, the concepts of logic are paid little attention in mathematics classes, due to the fact that their teaching is not prescribed in the new official syllabuses3. This is not the case of higher education, where a course on formal logic is oftengiven at the beginning of the year to first year university students, with a refreshing purpose. That course is not required in the syllabus, but some teachers see the need. Several scientific studies have shown that some of the difficulties encountered by studentswhile practicing mathematics come from their poor familiarity with concepts of logic. We assume that these students are insufficiently attended to by their teachers who think that the concepts are at their reach, since they are used in everyday life on the one hand, and they are gradually used in mathematical activities, on the other hand. In this thesis, we stand for the point that, for the concepts of logic to become real operational tools to a student who begins university studies, some teaching of these concepts which should address the connections with mathematical activities is necessary, at least as a starting point in higher education studies. To defend our thesis, we have divided our work into two parts which are as follows : In the first part, we present theoretical material necessary to our work as well as other technical tools that will be needed. We also provide a review of previous studies related to our issue. The second part is on an experiment we carried out with students from the Upper Sixth class - science option - of a high school in Yaoundé (Cameroon), and with first year university students of mathematics of the Yaoundé Higher Teachers’ Training College. This experiment had two stages : Firstly, the high school students and the university students filled out a questionnaire on logic and language. Following this, we organized a follow-up module involving 8 students purposely selected from their answers to the questionnaire. This questionnaire enabled us to detect meaningful points on how high school and university students grasp the concepts of logic, and the module helped to start debates which enabled in some cases to refine our analysis, and also provided us with strategic approaches forexplaining certain concepts of logic.

Le système de types de la logique d'ordre supérieur permet d'exclure certaines expressions indésirables telles que l'application d'un prédicat à lui-même. Cependant, il ne suffit pas pour vérifier des critères plus complexes comme l'absence de divisions par zéro. Cette thèse est consacrée à l’étude d’une extension de la logique d’ordre supérieur appelée sous-typage par prédicats (predicate subtyping), dont l'objet est de rendre l'attribution de types aussi expressive que l'attribution de prédicats. A partir d'un type A et d'un prédicat P(x) de domaine A, le sous-typage par prédicats permet de construire un sous-type de A, noté {x : A | P(x)}, dont les éléments sont les termes t de type A tels que P(t) est démontrable. Le sous-typage par prédicats est au coeur du système PVS.Ce travail présente la formalisation d'un système minimal incluant le sous-typage par prédicats, appelé PVS-Core, ainsi qu'un système de certificats vérifiables pour PVS-Core. Ce deuxième système, appelé PVS-Cert, repose sur l'introduction de termes de preuves et de coercions explicites. PVS-Core et PVS-Cert sont munis d'une notion de conversion correspondant respectivement à l'égalité modulo beta et à l'égalité modulo beta et effacement des coercions, choisi pour établir une correspondance simple entre les deux systèmes.La construction de PVS-Cert est semblable à celle des PTS (Pure Type Systems) avec paires dépendantes et PVS-Cert peut être muni de la notion de beta-sigma-réduction utilisée au coeur de ces systèmes. L'un des principaux théorèmes démontré dans ce travail est la normalisation forte de la réduction sous-jacente à la conversion et de la beta-sigma-réduction. Ce théorème permet d'une part de construire un algorithme de vérification du typage (et des preuves) pour PVS-Cert et d'autre part de démontrer un résultat d'élimination des coupures, utilisé à son tour pour prouver plusieurs propriétés importantes des deux systèmes étudiés. Par ailleurs, il est également démontré que PVS-Cert est une extension conservative du PTS lambda-HOL, et qu'en conséquence PVS-Core est une extension conservative de la logique d'ordre supérieur.Une deuxième partie présente le prototype d'une instrumentation de PVS pour produire des certificats de preuve. Une troisième et dernière partie est consacrée à l'étude de liens entre logique classique et constructive avec la définition d'une traduction par double négation minimale ainsi que la présentation d'un algorithme de constructivisation automatique des preuves. / The type system of higher-order logic allows to exclude some unexpected expressions such as the application of a predicate to itself. However, it is not sufficient to verify more complex criteria such as the absence of divisions by zero. This thesis is dedicated to the study of an extension of higher-order logic, named predicate subtyping, whose purpose is to make the assignment of types as expressive as the assignment of predicates. Starting from a type A and a predicate P(x) of domain A, predicate subtyping allows to build a subtype of A, denoted {x : A | P(x)}, whose elements are the terms t of type A such that P(t) is provable. Predicate subtyping is at the heart of the proof system PVS.This work presents the formalization of a minimal system expressing predicate subtyping, named PVS-Core, as well as a system of verifiable certificates for PVS-Core. This second system, named PVS-Cert, is based on the introduction of proof terms and explicit coercions. PVS-Core and PVS-Cert are equipped with a notion of conversion corresponding respectively to equality modulo beta and to equality modulo beta and the erasure of coercions, chosen to establish a simple correspondence between the two systems.The construction of PVS-Cert is similar to that of PTSs (Pure Type Systems) with dependent pairs and PVS-Cert can be equipped with the notion of beta-sigma-reduction used at the core of these systems. One of the main theorems proved in this work is the strong normalization of both the reduction underlying the conversion and beta-sigma-reduction. This theorem allows, on the one hand, to build a type-checking (and proof-checking) algorithm for PVS-Cert and, on the other hand, to prove a cut elimination result, used in turn to prove important properties of the two studied systems. Furthermore, it is also proved that PVS-Cert is a conservative extension of the PTS lambda-HOL and that, as a consequence, PVS-Core is a conservative extension of higher-order logic.A second part presents the prototype of an instrumentation of PVS to generate proof certificates. A third and final part is dedicated to the study of links between classical and constructive logic, with the definition of a minimal double-negation translation as well as the presentation of an automated proof constructivization algorithm.

The focus of current formal verification methods is mitigating the state explosion problem. One of these formal methods is predicate abstraction, which reduces concrete states of a system to bitvectors of true/false valuations of a set of predicates. Predicate abstraction comes in two flavors, over-approximation and under-approximation. A drawback of over-approximation is that it produces too many spurious errors for data-intensive applications. A more recent under-approximation technique which does not produce spurious errors, does abstract matching on concrete states (AMCS). AMCS adds behaviors to an abstract system by augmenting the set of initial predicates, making use of a theorem prover. The logic behind this approach is that if an error is found in the early coarse abstractions of the system, we save space and time. Our research improves AMCS by providing a refinement technique which guarantees termination. Our technique finds errors in less time and space by using an abstract state splitting algorithm based on intervals, which does not require a theorem prover.

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The verification problem for action logic programs with non-terminating behaviour is in general undecidable. In this paper, we consider a restricted setting in which the problem becomes decidable. On the one hand, we abstract from the actual execution sequences of a non-terminating program by considering infinite sequences of actions defined by a Büchi automaton. On the other hand, we assume that the logic underlying our action formalism is a decidable description logic rather than full first-order predicate logic.

Die Erfoschung informationsstruktureller Ausdrucksformen hat in den letzten Jahrzehnten stark an Bedeutung gewonnen. Der Schwerpunkt liegt dabei auf der Untersuchung von Universalien, die der Kennzeichnung von “alten/bekannten” und “neuen/wichtigen” Informationen dienen. Auch wenn die Forschung diesem Thema bereits viel Raum gegeben hat, weiß man heute immer noch sehr wenig über die Realisierungsmöglichkeiten von Topik und Fokus in schlecht dokumentierten Sprachen. Die vorliegende Dissertation leistet mit der Diskussion über die Fokusmarkierungsstrategien einer kleinen Sprachfamilie im Herzen Afrikas einen wichtigen Beitrag zur informationsstrukturellen Grundlagenforschung. Sie gibt einen Überblick über die Realisierungsmöglichkeiten von Topik und Fokus in sechs genealogisch verwandten Sprachen der Sara-Bagirmi-Gruppe (BAGIRMI, KENGA, MBAY, KABBA, NGAMBAY und SAR) und konzentriert sich dabei auf die Untersuchung der prädikatszentrierten Fokustypen. Diese bestehen aus i) Fokus auf der lexikalischen Bedeutung des Verbes, ii) Fokus auf dem Polaritätsoperator („Verum-Fokus“) und iii) Fokus auf dem Tempus-Aspekt-Modus-Operator. Die Arbeit beleuchtet somit nicht nur die grammatische Stuktur unzureichend untersuchter Sprachen, sie liefert mit dem Schwerpunkt auf Nichttermfokus auch Einblick in ein vernachlässigtes Forschungsfeld. Die Untersuchungen im Rahmen der Dissertation zeigen, dass die Sara-Bagirmi-Sprachen eine Vielzahl verschiedener Fokussierungsstrategien aufweisen. Obwohl alle sechs Sprachen zu einer Familie gehören, unterscheiden sich die vorhandenen Strategien formal und teilweise auch funktional voneinander. Der innerfamiliäre Vergleich der Gemeinsamkeiten und der Unterschiede erlaubt zum einen Rückschlüsse auf die Beziehung zwischen Form und Funktion im Allgemeinen. Zum anderen ermöglicht er konkrete Aussagen zur diachronen Entwicklung der ausgewählten Konstruktionen. Die Korpusstudie zu einer der Sprachen ergänzt die Forschungsarbeit. Sie stellt ausgewählte Merkmale der Fokusrealisierung vor und zeigt den Gebrauch der präsentierten Strategien im natürlichen Diskurs. Die vorliegende Dissertation komplettiert die Datenbasis der empirischen Sprachforschung und bereichert mit ihren Ergebnissen die Sprachtheorie um wertvolle Erkenntnisse. So belegt z.B. die Analyse der Fokussierungsstrategien des Sara-Bagirmi die enge Verbindung zwischen prädikatszentrierten Fokustypen und TAM-basierten Kategorien. Sie zeigt außerdem, dass die Klassifikation der prädikatszentrierten Fokustypen neu überdacht werden sollte, da einige der untersuchten Sprachen neben den o.g. Typen auch grammatikalisierte Formen von Intensivierung oder Formen von „Gewissheit“ aufweisen. / The development of information structue and its expression has become increasingly important in the recent decades. The main focus is on the investigation of linguistic universals that are used to identify “old/given” and “new/important” information. Despite of a body of literature on this issue, little is known about the possibilities of realization of topic and focus in poorly documented languages. This investigation contributes to basic informational research in the field of information on the focus marking strategies of a small language family in the heart of Africa. It gives an overview of the way in which topic and focus are implemented in six genealogically related languages of Sara-Bagirmi (BAGIRMI, KENGA, MBAY, KABBA, NGAMBAY and SAR). The focus is on the investigation of predicate-centered focus types. These consist of i) focus on the lexical meaning of the verb, ii) focus on the polarity operator (“truth-value focus”), and iii) focus on the tense-aspect-mode operator. The work thus not only illuminates the grammatical structure of insufficiently studied languages, but also provides an insight into a neglected field of research with emphazising non-term focus. The results show that the Sara-Bagirmi languages have a variety of different focus strategies. Although all six languages belong to one family, the existing strategies differ formally and partly functionally from each other. The inter-familiar comparison of the similarities and the differences allows, on the one hand, conclusions about the relationship between form and function in general. On the other hand, it makes concrete statements on the diachronic development of the selected constructions. The corpus study on one of the languages complements the research work. It presents selected features of the focus realization and shows the use of the presented strategies in natural discourse. This dissertation completes the database of empirical linguistic research and enriches the theory of language with valuable results. Thus, for example, the analysis of the focusing strategies in Sara-Bagirmi confirms the close relationship of predicate-centered focus types and TAM-based categories. It also shows that the classification of the predicate-centered focus types should be reconsidered, since some of the examined languages in addition to the abovementioned types have grammaticalized forms of “intensification” or “definiteness/ certainty”.

This thesis deals with syntactic relation of subject-predicate agreement in Czech, concentrating on special cases. The theoretical part describes the term "agreement" in terms of the traditional dependency approach, presents the definition of the term and specifies its width. It describes the subject-predicate agreement from from other theoretical perspectives, too (for example generative grammar analysis etc.). The main part of this theoretical chapter contains particular cases of subject-predicate agreement, as described in Czech grammars and textbooks. However, this description does not take into account all options and variants of agreement used in everyday conversation. Therefore, we investigate the problem of agreement through an empirical survey, which serves us to identify more complex cases (multiple subject with disjunctive, adversative and compared relation between its constituents; based on the cases found in the Czech National Corpus). Another source of data comes from a questionnaire, which maps how complex agreement structures are acquired by users of the language (students of the Faculty of Arts, Charles University). The data found in Czech National Corpus enable us to specify tendencies of agreement in more complicated cases; these tendencies should be included in the grammatical...

Diese Dissertation untersucht die lexikalischen und morphosyntaktischen Eigenschaften polnischer und russischer Prädikatsnomina sowie der Kopula (des Kopulalexems). Sie stellt die Kasusvariation (Nominativ vs. Instrumental) sowie die Formvariation (Kurz- vs. Langformadjektiv) an diesen Prädikativen in den Mittelpunkt und hat das Ziel, ihre grammatische Quelle, Funktionsweise und Interpretation bzw. Lesart zu erklären. Dabei werden sowohl die primäre als auch die sekundäre Prädikation betrachtet. Im Rahmen der Formulierung der theoretischen Grundlagen wird ein Vorschlag gemacht, der es gestattet, den viel diskutierten Begriff "Prädikation" referenzsemantisch zu erfassen. Ferner wird vorgeschlagen, Flexionsmorphologie und Semantik (im Sinne von "grammatischer Bedeutung") voneinander zu trennen. In diesem Sinne leistet die vorgelegte Dissertation auch einen Beitrag zur Forschung über die Schnittstelle zwischen Morphosyntax und Semantik.

Indiana University-Purdue University Indianapolis (IUPUI) / The amount of information produced in the form of electronic free text in healthcare is increasing to levels incapable of being processed by humans for advancement of his/her professional practice. Information extraction (IE) is a sub-field of natural language processing with the goal of data reduction of unstructured free text. Pertinent to IE is an annotated corpus that frames how IE methods should create a logical expression necessary for processing meaning of text. Most annotation approaches seek to maximize meaning and knowledge by chunking sentences into phrases and mapping these phrases to a knowledge source to create a logical expression. However, these studies consistently have problems addressing semantics and none have addressed the issue of semantic similarity (or synonymy) to achieve data reduction. To achieve data reduction, a successful methodology for data reduction is dependent on a framework that can represent currently popular phrasal methods of IE but also fully represent the sentence. This study explores and reports on the benefits, problems, and requirements to using the predicate-argument statement (PAS) as the framework. A convenient sample from a prior study with ten synsets of 100 unique sentences from radiology reports deemed by domain experts to mean the same thing will be the text from which PAS structures are formed.

This study focuses on the predicate argument structure (PAS) of a sub-class of verbs in Xitsonga - verbs of change of possession: give, contribute, future having, providing, obtaining and verbs of exchange. It is shown that these verbs select various theta roles to form their PAS in the different alternations allowed in this language. The effects of the applicative {-el-} and causative {-is-} verbal affixes on the PAS of such verbs are also considered. The study confirms the fact that the ordering of objects in ditransitive verbs is determined by an interplay of syntactic and semantic factors. Ambiguity arises in the case of two animate objects. In this case the object with a definite reading will appear adjacent to the verb. / African Languages / M. A. (Arican Languages)