14 research outputs found

    Weak Type Theory : a formal language for mathematics

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    Terminological Methods in Lexicography: Conceptualising, Organising, and Encoding Terms in General Language Dictionaries

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    Os dicionários de língua geral apresentam inconsistências de uniformização e cientificidade no tratamento do conteúdo lexicográfico especializado. Analisando a presença e o tratamento de termos em dicionários de língua geral, propomos um tratamento mais uniforme e cientificamente rigoroso desse conteúdo, considerando também a necessidade de compilar e alinhar futuros recursos lexicais em consonância com padrões interoperáveis. Partimos da premissa de que o tratamento dos itens lexicais, sejam unidades lexicais (palavras em geral) ou unidades terminológicas (termos ou palavras pertencentes a determinados domínios), deve ser diferenciado, e recorremos a métodos terminológicos para tratar os termos dicionarizados. A nossa abordagem assume que a terminologia – na sua dupla dimensão linguística e conceptual – e a lexicografia, como domínios interdisciplinares, podem ser complementares. Assim, apresentamos objetivos teóricos (aperfeiçoamento da metalinguagem e descrição lexicográfica a partir de pressupostos terminológicos) e práticos (representação consistente de dados lexicográficos), que visam facilitar a organização, descrição e modelização consistente de componentes lexicográficos, nomeadamente a hierarquização das etiquetas de domínio, que são marcadores de identificação de léxico especializados. Queremos ainda facilitar a redação de definições, as quais podem ser otimizadas e elaboradas com maior precisão científica ao seguir uma abordagem terminológica no tratamento dos termos. Analisámos os dicionários desenvolvidos por três instituições académicas distintas: a Academia das Ciências de Lisboa, a Real Academia Española e a Académie Française, que representam um valioso legado da tradição lexicográfica académica europeia. A análise inicial inclui um levantamento exaustivo e a comparação das etiquetas de domínio usadas, bem como um debate sobre as opções escolhidas e um estudo comparativo do tratamento dos termos. Elaborámos, depois, uma proposta metodológica para o tratamento de termos em dicionários de língua geral, tomando como exemplo dois domínios, GEOLOGIA e FUTEBOL, extraídos da edição de 2001 do dicionário da Academia das Ciências de Lisboa. Revimos os termos selecionados de acordo com os princípios terminológicos defendidos, dando origem a sentidos especializados revistos/novos para a primeira edição digital deste dicionário. Representamos e anotamos os dados usando as especificações da TEI Lex-0, uma extensão da TEI (Text Encoding Initiative), dedicada à codificação de dados lexicográficos. Destacamos também a importância de ter etiquetas de domínio hierárquicas em vez de uma lista simples de domínios, vantajosas para a organização dos dados, correspondência e possíveis futuros alinhamentos entre diferentes recursos lexicográficos. A investigação revelou que a) os modelos estruturais dos recursos lexicais são complexos e contêm informação de natureza diversa; b) as etiquetas de domínio nos dicionários gerais da língua são planas, desequilibradas, inconsistentes e, muitas vezes, estão desatualizadas, havendo necessidade de as hierarquizar para organizar o conhecimento especializado; c) os critérios adotados para a marcação dos termos e as fórmulas utilizadas na definição são díspares; d) o tratamento dos termos é heterogéneo e formulado de diferentes formas, pelo que o recurso a métodos terminológicos podem ajudar os lexicógrafos a redigir definições; e) a aplicação de métodos terminológicos e lexicográficos interdisciplinares, e também de padrões, é vantajosa porque permite a construção de bases de dados lexicais estruturadas, concetualmente organizadas, apuradas do ponto de vista linguístico e interoperáveis. Em suma, procuramos contribuir para a questão urgente de resolver problemas que afetam a partilha, o alinhamento e vinculação de dados lexicográficos.General language dictionaries show inconsistencies in terms of uniformity and scientificity in the treatment of specialised lexicographic content. By analysing the presence and treatment of terms in general language dictionaries, we propose a more uniform and scientifically rigorous treatment of this content, considering the necessity of compiling and aligning future lexical resources according to interoperable standards. We begin from the premise that the treatment of lexical items, whether lexical units (words in general) or terminological units (terms or words belonging to particular subject fields), must be differentiated, and resort to terminological methods to treat dictionary terms. Our approach assumes that terminology – in its dual dimension, both linguistic and conceptual – and lexicography, as interdisciplinary domains, can be complementary. Thus, we present theoretical (improvement of metalanguage and lexicographic description based on terminological assumptions) and practical (consistent representation of lexicographic data) objectives that aim to facilitate the organisation, description and consistent modelling of lexicographic components, namely the hierarchy of domain labels, as they are specialised lexicon identification markers. We also want to facilitate the drafting of definitions, which can be optimised and elaborated with greater scientific precision by following a terminological approach for the treatment of terms. We analysed the dictionaries developed by three different academic institutions: the Academia das Ciências de Lisboa, the Real Academia Española and the Académie Française, which represent a valuable legacy of the European academic lexicographic tradition. The initial analysis includes an exhaustive survey and comparison of the domain labels used, as well as a debate on the chosen options and a comparative study of the treatment of the terms. We then developed a methodological proposal for the treatment of terms in general language dictionaries, exemplified using terms from two domains, GEOLOGY and FOOTBALL, taken from the 2001 edition of the dictionary of the Academia das Ciências de Lisboa. We revised the selected terms according to the defended terminological principles, giving rise to revised/new specialised meanings for the first digital edition of this dictionary. We represent and annotate the data using the TEI Lex-0 specifications, a TEI (Text Encoding Initiative) subset for encoding lexicographic data. We also highlight the importance of having hierarchical domain labels instead of a simple list of domains, which are beneficial to the data organisation itself, correspondence and possible future alignments between different lexicographic resources. Our investigation revealed the following: a) structural models of lexical resources are complex and contain information of a different nature; b) domain labels in general language dictionaries are flat, unbalanced, inconsistent and often outdated, requiring the need to hierarchise them for organising specialised knowledge; c) the criteria adopted for marking terms and the formulae used in the definition are disparate; d) the treatment of terms is heterogeneous and formulated differently, whereby terminological methods can help lexicographers to draft definitions; e) the application of interdisciplinary terminological and lexicographic methods, and of standards, is advantageous because it allows the construction of structured, conceptually organised, linguistically accurate and interoperable lexical databases. In short, we seek to contribute to the urgent issue of solving problems that affect the sharing, alignment and linking of lexicographic data

    Koherenssiteorian perusteista

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    In the thesis I study various quantum coherence phenomena and create some of the foundations for a systematic coherence theory. So far, the approach to quantum coherence in science has been purely phenomenological. In my thesis I try to answer the question what quantum coherence is and how it should be approached within the framework of physics, the metatheory of physics and the terminology related to them. It is worth noticing that quantum coherence is a conserved quantity that can be exactly defined. I propose a way to define quantum coherence mathematically from the density matrix of the system. Degenerate quantum gases, i.e., Bose condensates and ultracold Fermi systems, form a good laboratory to study coherence, since their entropy is small and coherence is large, and thus they possess strong coherence phenomena. Concerning coherence phenomena in degenerate quantum gases, I concentrate in my thesis mainly on collective association from atoms to molecules, Rabi oscillations and decoherence. It appears that collective association and oscillations do not depend on the spin-statistics of particles. Moreover, I study the logical features of decoherence in closed systems via a simple spin-model. I argue that decoherence is a valid concept also in systems with a possibility to experience recoherence, i.e., Poincaré recurrences. Metatheoretically this is a remarkable result, since it justifies quantum cosmology: to study the whole universe (i.e., physical reality) purely quantum physically is meaningful and valid science, in which decoherence explains why the quantum physical universe appears to cosmologists and other scientists very classical-like. The study of the logical structure of closed systems also reveals that complex enough closed (physical) systems obey a principle that is similar to Gödel's incompleteness theorem of logic. According to the theorem it is impossible to describe completely a closed system within the system, and the inside and outside descriptions of the system can be remarkably different. Via understanding this feature it may be possible to comprehend coarse-graining better and to define uniquely the mutual entanglement of quantum systems.Väitöskirjassani käsittelen erilaisia kvanttikoherenssi-ilmiöitä ja luon perusteita systemaattiselle koherenssiteorialle. Kvanttikoherenssin käsittely tieteessä on tähän asti ollut puhtaasti fenomenologista. Väitöstutkimuksessani pyrin vastaamaan kysymykseen, mitä kvanttikoherenssi on ja miten sitä tulee lähestyä fysiikan, fysiikan metateorian ja niihin liittyvän terminologian kannalta. Erityisen huomionarvoista on, että kvanttikoherenssi on säilyvä suure, joka voidaan määrittää eksaktisti. Esitän tavan määrittää kvanttikoherenssi matemaattisesti systeemin tiheysmatriisista. Degeneroituneet kvanttikaasusysteemit eli Bose-kondensaatit ja ultrakylmät fermionisysteemit muodostavat hyvän koherenssitutkimuslaboratorion, sillä niiden entropia on pieni ja koherenssi suuri, joten niissä esiintyvät koherenssi-ilmiötkin ovat voimakkaita. Väitöstutkimuksessani käsittelen degeneroituneissa kvanttikaasuissa tapahtuvien koherenssi-ilmiöiden osalta lähinnä kollektiivista assosiaatiota atomeista molekyyleiksi, Rabi-oskillaatioita ja dekoherenssia. Osoittautuu, että kollektiivinen assosiaatio ja oskillaatiot eivät riipu hiukkasten spin-statistiikasta. Lisäksi selvitän suljetun systeemin dekoherenssin loogisia piirteitä yksinkertaisen spin-mallin avulla. Väitän, että dekoherenssi on pätevä käsite myös niissä tapauksissa, joissa systeemillä on mahdollisuus rekoherenssiin eli Poincarén paluut ovat mahdollisia. Tämä on metateoreettisesti merkittävä tulos, sillä se oikeuttaa kvanttikosmologian: koko maailmankaikkeuden (siis fysikaalisen todellisuuden) puhdas kvanttifysikaalinen tarkastelu on mielekästä ja pätevää tiedettä, jossa dekoherenssi selittää, miksi kvanttifysikaalinen maailmankaikkeus näyttäytyy maailmankaikkeuden tutkijoille hyvin klassisen kaltaisena. Suljetun systeemin loogisen rakenteen tutkiminen paljastaa myös, että riittävän monimutkaisille (fysikaalisille) suljetuille systeemeille pätee logiikasta tutun Gödelin epätäydellisyysteoreeman kaltainen periaate, jonka mukaan suljetun systeemin täydellinen kuvaaminen systeemin sisältä katsoen on mahdotonta, ja että suljetun systeemin sisäpuolinen ja ulkopuolinen kuvaus systeemistä voivat poiketa merkittävästi toisistaan. Tämän ymmärtämisen myötä voi olla mahdollista ymmärtää karkeistusta paremmin ja määritellä kvanttifysikaalisten systeemien keskinäinen lomittuminen yksikäsitteisesti

    Meaning construction in popular science : an investigation into cognitive, digital, and empirical approaches to discourse reification

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    This thesis uses cognitive linguistics and digital humanities techniques to analyse abstract conceptualization in a corpus of popular science texts. Combining techniques from Conceptual Integration Theory, corpus linguistics, data-mining, cognitive pragmatics and computational linguistics, it presents a unified approach to understanding cross-domain mappings in this area, and through case studies of key extracts, describes how concept integration in these texts operates. In more detail, Part I of the thesis describes and implements a comprehensive procedure for semantically analysing large bodies of text using the recently- completed database of the Historical Thesaurus of English. Using log-likelihood statistical measures and semantic annotation techniques on a 600,000 word corpus of abstract popular science, this part establishes both the existence and the extent of significant analogical content in the corpus. Part II then identifies samples which are particularly high in analogical content from the corpus, and proposes an adaptation of empirical and corpus methods to support and enhance conceptual integration (sometimes called conceptual blending) analyses, informed by Part I’s methodologies for the study of analogy on a wider scale. Finally, the thesis closes with a detailed analysis, using this methodology, of examples taken from the example corpus. This analysis illustrates those conclusions which can be drawn from such work, completing the methodological chain of reasoning from wide-scale corpora to narrow-focus semantics, and providing data about the nature of highly-abstract popular science as a genre. The thesis’ original contribution to knowledge is therefore twofold; while contributing to the understanding of the reification of abstractions in discourse, it also focuses on methodological enhancements to existing tools and approaches, aiming to contribute to the established tradition of both analytic and procedural work advancing the digital humanities in the area of language and discourse

    Human reasoning and cognitive science

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    In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain

    Réalisabilité et paramétricité dans les systèmes de types purs

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    Cette thèse porte sur l adaptation de la réalisabilité et la paramétricité au cas des types dépendants dans le cadre des Systèmes de Types Purs. Nous décrivons une méthode systématique pour construire une logique à partir d un langage de programmation, tous deux décrits comme des systèmes de types purs. Cette logique fournit des formules pour exprimer des propriétés des programmes et elle offre un cadre formel adéquat pour développer une théorie de la réalisabilité au sein de laquelle les réalisateurs des formules sont exactement les programmes du langage de départ. Notre cadre permet alors de considérer les théorèmes de représentation pour le système T de Gödel et le système F de Girard comme deux instances d'un théorème plus général.Puis, nous expliquons comment les relations logiques de la théorie de la paramétricité peuvent s'exprimer en terme de réalisabilité, ce qui montre que la logique engendrée fournit un cadre adéquat pour développer une théorie de la paramétricité du langage de départ. Pour finir, nous montrons comment cette théorie de la paramétricité peut-être adaptée au système sous-jacent à l'assistant de preuve Coq et nous donnons un exemple d'application original de la paramétricité à la formalisation des mathématiques.This thesis focuses on the adaptation of realizability and parametricity to dependent types in the framework of Pure Type Systems. We describe a systematic method to build a logic from a programming language, both described as pure type systems. This logic provides formulas to express properties of programs and offers a formal framework that allows us to develop a theory of realizability in which realizers of formulas are exactly programs of the starting programming language. In our framework, the standard representation theorems of Gödel's system T and Girard's system F may be seen as two instances of a more general theorem. Then, we explain how the so-called logical relations of parametricity theory may be expressed in terms of realizability, which shows that the generated logic provides an adequate framework for developping a general theory of parametricity. Finally, we show how this parametricity theory can be adapted to the underlying type system of the proof assistant Coq and we give an original example of application of parametricity theory to the formalization of mathematics.LYON-ENS Sciences (693872304) / SudocSudocFranceF
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