<p>This thesis deals with different aspects towards many-valued unification which have been studied in the scope of category theory. The main motivation of this investigation comes from the fact that in logic programming, classical unification has been identified as the provision of coequalizers in Kleisli categories of term monads. Continuing in that direction, we have used categorical instrumentations to generalise the classical concept of a term. It is expected that this approach will provide an appropriate formal framework for useful developments of generalised terms as a basis for many-valued logic programming involving an extended notion of terms.</p><p>As a first step a concept for generalised terms has been studied. A generalised term is given by a composition of monads that again yields a monad, i.e. compositions of powerset monads with the term monad provide definitions for generalised terms. A composition of monads does, however, not always produce a monad. In this sense, techniques for monads composition provide a helpful tool for our concerns and therefore the study of these techniques has been a focus of this research.</p><p>The composition of monads make use of a lot of equations. Proofs become complicated, not to mention the challenge of understanding different steps of the equations. In this respect, we have studied visual techniques and show how a graphical approach can provide the support we need.</p><p>For the purpose of many-valued unification, similarity relations, generalised substitutions and unifiers have been defined for generalised terms.</p>

This thesis deals with different aspects towards many-valued unification which have been studied in the scope of category theory. The main motivation of this investigation comes from the fact that in logic programming, classical unification has been identified as the provision of coequalizers in Kleisli categories of term monads. Continuing in that direction, we have used categorical instrumentations to generalise the classical concept of a term. It is expected that this approach will provide an appropriate formal framework for useful developments of generalised terms as a basis for many-valued logic programming involving an extended notion of terms. As a first step a concept for generalised terms has been studied. A generalised term is given by a composition of monads that again yields a monad, i.e. compositions of powerset monads with the term monad provide definitions for generalised terms. A composition of monads does, however, not always produce a monad. In this sense, techniques for monads composition provide a helpful tool for our concerns and therefore the study of these techniques has been a focus of this research. The composition of monads make use of a lot of equations. Proofs become complicated, not to mention the challenge of understanding different steps of the equations. In this respect, we have studied visual techniques and show how a graphical approach can provide the support we need. For the purpose of many-valued unification, similarity relations, generalised substitutions and unifiers have been defined for generalised terms.

Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul / With the approaching end of Moore’s Law, where will not be possible to improve the capacity of silicon based processors, the quantum computing appear to be a good choice to provide a new era of computation. Quantum computing can be understood as the art of transform information encoded in the state of a quantum physical system. This encoding is through the quantum bits (qubits), which can be on superposition or entangled states, enabling to explore the property called quantum parallelism. In this work is discussed the creation of a quantum programming language implementing the object-oriented paradigm (OO), allowing manipulation of classes and objects, where the quantum effects are handled through a monadic approach, extending the Featherweight Java (FJ) proposal. This language is formally defined through the operational semantics, which allow the implementation in any language that provides closures. That language formalization enables us to create an interpreter, implementing the steps of lexical, syntactic and semantic analysis, focusing in the type system to embedded quantum computing concepts in a classical language. Several examples are provided in the text, showing ways to handle the monadic layer in order to perform transformations in quantum information. / Com a aproximação do fim da Lei de Moore, onde não será possível melhorar a capacidade dos processadores baseados em silício, a computação quântica aparece como uma boa escolha para prover uma nova era da computação. A computação quântica pode ser entendida como a arte de transformar informação codificada no estado físico quântico. Esta codificação se dá através de bits quânticos (qubits), que podem estar em estados de superposição ou emaranhados, permitindo explorar uma propriedade conhecida como paralelismo quântico. Nesta dissertação é discutida a criação de uma linguagem de programação quântica que utiliza-se do paradigma da orientação a objetos (OO), fornecendo a possibilidade de manipular classes e objetos, onde os dados e os efeitos quânticos são manipulados através de uma abordagem monádica, sendo modelada como uma extensão da proposta Featherweight Java (FJ). Esta extensão é definida formalmente através da apresentação de sua semântica operacional, a qual é passível de implementação em qualquer linguagem de programação que forneça o mecanismo de closures. A formalização desta linguagem permitiu a criação de um interpretador, que implementa as fases de análise léxica, sintática e semântica, com foco especial no tratamento do sistema de tipos para embutir conceitos de computação quântica em uma linguagem clássica. Vários exemplos são fornecidos no decorrer do texto, mostrando formas de manipular a camada monádica para realizar transformações em informações quânticas.

Back to Husserl: Reclaiming the Traditional Philosophical Context ofthe Phenomenological ‘Problem’ of the Other: Leibniz’s Monadology”. The internalmotivation that led Husserl to revise his early view of the pure Ego as empty ofessential content is traced to the end of explicating his reformulation of phenomenologyas the egology of the concrete transcendental Ego. The necessity ofrecasting transcendental phenomenology as a transcendental idealism that followsfrom this reformulation is presented and the appearance of transcendentalsolipsism of this idealism exposed as unfounded. That the ground of this exposureis Husserl’s phenomenological appropriation of Leibniz’s metaphysical insightsinto the problem of accounting for the plurality of monads, and, therefore, not theCartesian problem of the other mind, is presented as the key to reclaiming thetraditional philosophical context of the phenomenological problem of the other. / La motivación interna que llevó a Husserl a revisar su visión tempranadel Ego puro como vacío de contenido esencial puede rastrearse con el fin de explicarsu reformulación de la fenomenología como la egología del Ego trascendentalconcreto. Este artículo presenta la necesidad de replantear la fenomenologíatrascendental como un idealismo trascendental que se sigue de esta reformulación,y se expone como infundada la apariencia de solipsismo trascendentalde este idealismo. El presente artículo también se ocupa de mostrar que la basepara esta exposición es la apropiación fenomenológica que hace Husserl de laspenetrantes intuiciones metafísicas de Leibniz en torno al problema de cómoexplicar la pluralidad de mónadas, y, por lo tanto, no el problema cartesianode la otra mente. Esto es considerado clave para reclamar el contexto filosóficotradicional del problema fenomenológico del otro.

>Magister Scientiae - MSc / In this thesis, we construct the ultrafilter space of a topological space using ultrafilters as points, study some of its properties and describe a method of generating compactifications through the ultrafilter space. As part of investigating some properties of the ultrafilter space, we show that the ultrafilter space forms a monad in the category of topological spaces. Furthermore, we show that rendering the ultrafilter space suitably separated results in a generation of separated compactifications which coincide with some well-known compactifications. When the ultrafilter space is rendered T0 or sober, the resulting compactifications is a stable Compactifications. Rendering the ultrafilter space T2 or Tychono results in the Stone_ Cechcompactification

Our work applies the dataflow algorithm to an area outside its traditional scope: functional languages. Our approach relies on a monadic intermediate language that provides low-level, imperative features like computed jumps and explicit allocations, while at the same time supporting high-level, functional-language features like case discrimination and partial application. We prototyped our work in Haskell using the HOOPL library and this dissertation shows numerous examples demonstrating its use. We prove the efficacy of our approach by giving a novel description of the uncurrying optimization in terms of the dataflow algorithm, as well as a complete implementation of the optimization using HOOPL.

Made available in DSpace on 2014-06-11T19:26:19Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-07-27Bitstream added on 2014-06-13T20:27:02Z : No. of bitstreams: 1 vagna_r_me_mar.pdf: 434719 bytes, checksum: a428d91e5b541767ee3e4a6a8500c5a9 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Partindo do sistema leibniziano e tomando como fio condutor a questão da geração da vida, pretendemos indicar os motivos filosóficos que levaram Leibniz a apoiar os biólogos pré-formacionistas do século XVII. A idéia de embutimento (ou encaixamento) de um novo ser dentro do seu progenitor, defendida pela teoria pré-formacionista, traz como que um exemplo do mundo monádico leibniziano, no qual todos os acontecimentos futuros, inclusive a geração de novos seres, foram já estabelecidos por Deus no momento da criação. As investigações microscópicas desenvolvidas por biólogos da época, especialmente por Leeuwenhoeck, descrevem um mundo até então desconhecido e trazem uma comprovação experimental da concepção teórica leibniziana. / Coming from the Leibniz`s system and taking as thread the question of the generation of the life, we intend to indicate the philosophical reasons that had taken Leibniz to support the preformationist biologists from the 17th century. The idea of inlaying (or fitting) of a new being into its ancestor, defended by the preformationist theory, brings an example about Leibniz`s monads world, in which all the future events, also the generation of new beings, already had been established by God at the moment of the creation. Microscopic researches developed by biologists at this time, especially by Leeuwenhoek, describe an unknown world until then, and bring an experimental evidence of Leibniz`s theoretical conception.

Nous avons souhaité, dans notre thèse, poursuivre et approfondir une étude de la pensée leibnizienne commencée en Maîtrise et en D.E.A. Nous plaçant à la frontière de la philosophie et de la littérature, nous nous sommes intéressé au point de vue d'un romancier leibnizien, Hermann Hesse (1877-1962), dont l'oeuvre imposante présente de multiples correspondances avec les théories leibniziennes. Nous avons construit notre étude autour des notions d’existence et d’harmonie, qui, dans la pensée de Hesse, comme, bien sûr, dans le système de Leibniz, sont des concepts fondamentaux. En mettant en lumière les différents thèmes leibniziens sous-jacents à la pensée poétique de Hesse, nous avons examiné le sens que prend la métaphysique de Leibniz dans un univers littéraire échappant, au premier abord, à la rationalisation.L’analyse des notions d’existence et d’harmonie nous a amené à définir les concepts, essentiels chez Leibniz, d’entr’expression et de communication, ainsi que ceux d’optimisme et de liberté. Dans l’univers leibnizien, univers "kaleidoscopique", lieu de concomitances et d’interactions multiples, l’individu, quoique déterminé dans son essence et se développant dans une forme d'autarcie, n’existe que par son inclusion dans l’ensemble du monde auquel il appartient. Nous avons essayé de montrer l'omniprésence des concepts leibniziens chez Hesse, qui conçoit le monde comme un tissu de correspondances et de résonances subtiles, gouvernées par l’immanence d’un Etre supérieur. Telle la monade leibnizienne, l’individu hessien recèle en lui-même une infinité de possibles, qu’il lui appartient d'explorer et de développer, pour acquérir son propre bonheur. La quête d’une certaine forme d'eudémonisme, qui constitue la base des interrogations fondamentales de l’œuvre hessienne, illustre sur un plan existentiel le thème leibnizien de l’optimisme. Chez Hesse, l’homme est à la recherche d’un art de vivre qui puisse lui procurer l'épanouissement de son être et la sérénité. Aspirant à un équilibre intérieur, à une communication avec le monde extérieur - et peut-être avec un principe divin - il recherche sa place au sein d'une harmonie universelle. / The aim of this thesis, is to pursue and examine thoroughly the study of the leibnizian thought we began to process in our Mastership and D.E.A. Looking at the frontier between philosophy and literature, we develop the viewpoint of the leibnizian novelist, Hermann Hesse (1877-1962), whose impressive work offers numerous connections with leibnizian theory. We based our study on the main notions of existence and harmony, which are both important concepts in the works of Leibniz and Hesse. Throwing light on some underlying leibnizian subjects in Hessian poetic thought, we examine the impact of leibnizian metaphysics in the literary universe of Hesse, which, at first sight, escapes to rationality.Analysing the notions of existence and harmony in Hesse and Leibniz leads to define precisely some leibnizian concepts which are very essential ones : expression ( of bodies, minds, universe…), communication, conception of freedom, optimism. In the leibnizian universe, which is a "kaleidoscopic" one and a site where numerous interactions and concomitances take place, the individual, though being determined in his essence as a "monad", i.e. a completely self-sufficient entity, only exists by inclusion in the whole world it belongs to. We tried to reveal the omnipresence of a number of leibnizian concepts in Hesse, who conceives the world as a set of correlations and subtle resonances, governed by an immanent superior Being. Like the leibnizian monad, the hessian individual contains in himself infinite possibilities, which it is his own responsability to explore and develop, in the view of making the experience of happiness. The search for a kind of eudemonism, which constitutes a basic question in the hessian work, is also an existential instanciation of the philosophical concept of optimism, a leibnizian subject. In Hesse's work, man is in search of an art of living, which can make him get self-fulfilment and absolute serenity. Longing for a mental balance, and for a true communication with the outer world – maybe with some divine principle – he is searching his niche in life, in its universal harmony.

This work deals with a basic question of modern science and it is its indefectibility. Quality of education is reduce to an evaluation of conformity to a common known knowledge and its quantity representation. Seeds of this long process go back to an ancient academia of Gondisapur established in an Arabic world. Author proclaims that the main goal of philosophy is to show, that this is not the only way of thinking and in the same time that the main goal and power of phenomenology is to apply the transcendental epoche to overcame the truth in its regularization shape. The hardcore of modern science is located in the world of mathematics and a lot of thinkers find the Math as a land of pure sureness - the core of this work in an opposite proofs, that in fact nowadays math is all, but the correct way of thinking. The two examples are explicit: the Pythagorean Theorem and the Sum of the geometric row. This work brings a quite new view on the mathematical problem of "the point" and "the nothing" as a border of things. In the second part uses as a frame of its topic the first 18 §§ of the work "Paradoxes of the infinite" by Czech mathematician of German mother tongue Bernard Bolzano. The important idea of this study is a new ontological view on the set of prime numbers.

The main purpose of this thesis is to combine the categorical approach to logic given by the study of doctrines, with the universal algebraic techniques given by the theory of the pseudo-monads and pseudo-distributive laws. Every completions of doctrines is then formalized by a pseudo-monad, and then combinations of these are studied by the analysis of the pseudo-distributive laws. The starting point are the works of Maietti and Rosolini, in which they describe three completions for elementary doctrines: the first which adds full comprehensions, the second comprehensive diagonals, and the third quotients. Then we determine the existential completion of a primary doctrine, and we prove that the 2-monad obtained from it is lax-idempotent, and that the 2-category of existential doctrines is isomorphic to the 2-category of algebras for this 2-monad. We also show that the existential completion of an elementary doctrine is again elementary and we extend the notion of exact completion of an elementary existential doctrine to an arbitrary elementary doctrine. Finally we present the elementary completion for a primary doctrine whose base category has finite limits. In particular we prove that, using a general results about unification for first order languages, we can easily add finite limits to a syntactic category, and then apply the elementary completion for syntactic doctrines. We conclude with a complete description of elementary completion for primary doctrine whose base category is the free product completion of a discrete category, and we show that the 2-monad constructed from the 2-adjunction is lax-idempotent.