A Probabilistic Data Model and Its Semantics

As database systems are increasingly being used in advanced applications, it is becoming common that data in these applications contain some elements of uncertainty. These arise from many factors, such as measurement errors and cognitive errors. As such, many researchers have focused on defining comprehensive uncertainty data models of uncertainty database systems. However, existing uncertainty data models do not adequately support some applications. Moreover, very few works address uncertainty tuple calculus. In this paper we advocate a probabilistic data model for representing uncertain information. In particular, we establish a probabilistic tuple calculus language and its semantics to meet the corresponding probabilistic relational algebra

Logic and logogrif in German idealism : an investigation into the notion of experience in Kant, Fichte, Schelling

In this thesis I investigate the notion of experience in German Idealist Philosophy. I focus on the exploration of an alternative to the transcendental model notion of experience through Schelling's insight into the notion of logogrif. The structural division of this project into two sections reflects the two theoretical standpoints of this project, namely the logic and the logogrif of experience. The first section - the logic of experience - explores the notion of experience provided in Kant's Critique of Pure Reason, Critique of Judgement and Fichte's Science of Knowledge. I argue that Kant's fundamental question about the possibility of synthetic a priori judgements succeeds in thematising the aporia of cognitive experience but results in a subject-oriented, representational model which radically confines the notion of experience to the constitutive laws of the understanding or to the normative precepts of Reason. Experience is founded upon a sharp division between faith and knowledge, will and logic, desire and reflection, absolute and finitude. Fichte's endeavour to articulate a non-representational account of experience, does not succeed in extricating itself from the representational model, so long as experience is reduced to the ever-producing deeds of the self-positing ego. Despite the serious differences between Kant's and Fichte's notions of experience, both accounts, so long as they unfold from a transcendental standpoint, attempt to resolve experience into conceptual laws or determinations of the ego's absolute will. Experience is transformed into an object of the subject's cognitive or volitional faculties. The paradoxes of man's interaction with the world are intended to be accommodated either by the law-giving spontaneity of the understanding and the Architectonic of Pure Reason or by the overpowerful primordial act of the self-positing ego. This implies the conceptualisation of the self in terms of constant identity-through-time, or sheer self-determination. However, this conceptualisation remains at the normative or prescriptive level, which in turn is projected upon the world. The latter, though appears as the subject's property, essentially remains alien and opaque, confirming the radical limitations of the ego rather than its order-giving authority. Moreover, this notion of experience is ultimately founded upon a radical expulsion of the divine from the world, the de-spiritualisation of the sensual and the de-sensualisation of the spiritual, the sharp juxtaposition between absolute and finitude. This results in a self-defeating subjectivity, whose firm identity and rule-giving authority does not rescue it from its perennial unattainability to 'organise the conditioned' or 'conquer the unconditioned'. In Kant's and Fichte's thought, however, I detect elements that potentially transgress their transcendental account of experience. These are found in Kant's concept of spontaneity and free play between understanding and imagination, and Fichte's concept of productivity. I argue that these elements lose their potential dynamism, so long as they are absorbed by the transcendental demands for the solution of the aporias of logic. However, these elements point to the need for a radical re-conceptualisation of the notion of experience. This is provided by means of Schelling's logogriflic approach, which constitutes the theme of the second section. The second section - the logogrif of experience - attempts to articulate a different approach towards the notion of experience, through an exploration of Schelling's versatile and provocative thought. This section focuses on Schelling's original insight into the notion and act of logogrif, which opens the dialogue between logos and mythos, cosmic becoming and human soul, cosmic imagination and human reflection, faith and knowledge. This section attempts to illuminate Schelling's fascinating philosophical investigations and discoveries that have been rather overlooked, possibly, due to Hegel's overwhelming critique. This section, after a brief critical examination of the Identity Philosophy, attempts to elucidate Schelling's notion of experience through his middle works, Of Human Freedom, Ages of the World, The Deities of Samothrace, which are treated as a self-developing trilogy. Schelling re-addresses the aporias of logic not as part of Reason's self-interrogation but as part of the cosmic paradoxes and living experiences. In this way, Schelling resets the scene of the debate on the conditions of possibility for cognitive experience by putting on the stage the enigmas of the cosmos and life rather than the Tribunal of Reason. Logic itself is conceived as a potency in the cosmic becoming, and consequently can no longer attempt to establish the transcendental conditions for the possibility of cognitive experience. Cosmic becoming, in which man is an active part, is conceived as the process of the movement, the interaction, the transformations and transmutations of multiple potencies. These, far beyond any mechanical conceptualisation, appear as self-moving and yet interdependent, unknown yet familiar, inscrutable and yet manifest powers, describing the mystery of life itself. The latter is depicted as an ever-recurrent act of longing for self-expression as active unity. Experience is conceived as the lived process of a network of living potencies, which may not only resist rational powers but may also puzzle and seize them. In this context, reflection acquires a plastic dimension, as opposed to its rigidity in the representational model of experience. Reflection depicts cosmic longing's self-formation, whose man is part. This self-bending formation partially illuminates the nature of longing, and from this standpoint is the logic of the longing. However, this formation is movable, transmutable and mostly ineffable, and from this standpoint is the logic of a riddle: a logogrif. Logogrif is the transitive term that attempts to describe the transition of experience from its enacted phase to its allusive conceptual utterance, and in this sense the term itself participates in both phases, as both form of thought and form of life. The logogrific approach to experience in turn transposes us as from the realm of pure concepts to the realm of the mystery of life, from pure thought to acts of longing, from the Architectonic of Pure Reason to Cosmic Theurgy. The latter term attempts to grasp the paradox and dynamism of cosmic and non-cosmic becoming by means of multiple, vanishing and ever-recurring, transmutable potencies, or in Schelling's terms 'the magic of insoluble life'. Schelling's logogrific account consists in a powerful voice for the re-enchantment of the world, the introduction into the notion of experience of the imminence of the divine. This is not suggested in terms of the adoption of old religious doctrines but by means of the discovery and re-discovery of the theurgy of life, through the intensification of our artistic mood, the creative expansion of our deeds. This notion of experience allows for the reconsideration of the notion of the self, in terms of a dynamic, conflictual process between conscious and unconscious powers and the critical revaluation of the accounts of subjectivity which reduce it to the sphere of self-consciousness. The thesis concludes with the need for an investigation into the relation between logos and mythos, which only tangentially has been introduced by the present project. In this context it will be possible to re-appraise the potential that the logogrific approach opens for an alternative to both logical and traditional mythological patterns of thinking

Reasoning reasonably in mathematics

Two tasks designed to encourage mathematical reasoning without any need for calculations were presented to students with the aim of seeking evidence of different forms of attention (Mason, 2003), and using these to learn about the tasks and about students’ power to reason ‘reasonably’ in mathematics. The first task that involves locating a secret place using an applet was solved by two pairs of grade 4 Portuguese students. The second task, involving the structure of magic squares, was proposed to two classes of Portuguese students, aged 12-13. The interactions between pairs of students and teacher probes were taped and transcribed, and, in the second one, students’ written responses were collected as well. In both cases, the data were analysed using the fivefold framework of microstructure of attention. The first case gives evidence that young students can reason ‘reasonably’ but that there are delicate shifts which may require sensitivity on the part of the teacher to help students progress. In the second case, the data analysis shows that these students displayed the power to reason ‘reasonably’ in mathematics, and that difficulties can be accounted for in terms of not only what was being attended to, but the form of that attention.Foram propostas duas tarefas a alunos portugueses do ensino básico para os encorajar a raciocinar matematicamente sem o recurso a cálculos, com o objetivo de procurar evidências sobre diferentes formas de atenção (Mason, 2003) e de usar essas evidências para refletir sobre as tarefas e sobre a capacidade dos alunos raciocinarem “com razoabilidade” em matemática. A primeira tarefa, centrada na localização de um lugar secreto usando uma applet, foi resolvida por dois pares de alunos do 4.º ano de escolaridade. A segunda, envolvendo a estrutura de quadrados mágicos, foi proposta a duas turmas do 7.º ano de escolaridade. Em qualquer dos casos, procedeu-se à gravação e transcrição das interações entre alunos e professor e na segunda tarefa recolheram-se, ainda, as resoluções escritas dos alunos. Os dados obtidos foram analisados usando um modelo composto por cinco formas ou microestruturas de atenção. No caso da primeira tarefa, evidencia-se que as crianças são capazes de raciocinar “com razoabilidade” mas que o seu progresso depende de mudanças subtis que requerem sensibilidade por parte do professor. A análise de dados relativos à segunda tarefa, revela, igualmente, que os alunos mostram poder para raciocinar “com razoabilidade”. Revela, ainda, que as suas dificuldades podem ser explicadas não só em termos daquilo que é o objeto da atenção mas também da forma desta atenção

Machine learning and its applications in reliability analysis systems

In this thesis, we are interested in exploring some aspects of Machine Learning (ML) and its application in the Reliability Analysis systems (RAs). We begin by investigating some ML paradigms and their- techniques, go on to discuss the possible applications of ML in improving RAs performance, and lastly give guidelines of the architecture of learning RAs. Our survey of ML covers both levels of Neural Network learning and Symbolic learning. In symbolic process learning, five types of learning and their applications are discussed: rote learning, learning from instruction, learning from analogy, learning from examples, and learning from observation and discovery. The Reliability Analysis systems (RAs) presented in this thesis are mainly designed for maintaining plant safety supported by two functions: risk analysis function, i.e., failure mode effect analysis (FMEA) ; and diagnosis function, i.e., real-time fault location (RTFL). Three approaches have been discussed in creating the RAs. According to the result of our survey, we suggest currently the best design of RAs is to embed model-based RAs, i.e., MORA (as software) in a neural network based computer system (as hardware). However, there are still some improvement which can be made through the applications of Machine Learning. By implanting the 'learning element', the MORA will become learning MORA (La MORA) system, a learning Reliability Analysis system with the power of automatic knowledge acquisition and inconsistency checking, and more. To conclude our thesis, we propose an architecture of La MORA

Regula Socratis: The Rediscovery of Ancient Induction in Early Modern England

A revisionist account of how philosophical induction was conceived in the ancient world and how that conception was transmitted, altered, and then rediscovered. I show how philosophers of late antiquity and then the medieval period came step-by-step to seriously misunderstand Aristotle’s view of induction and how that mistake was reversed by humanists in the Renaissance and then especially by Francis Bacon. I show, naturally enough then, that in early modern science, Baconians were Aristotelians and Aristotelians were Baconians

THE STUDY OF JURISPRUDENCE-A LETTER TO A HOSTILE STUDENT

The value to the law student of a course in jurisprudence has long been a question mark-and to the teachers as well as the students. The students have not been prompted by self-interest, as the teachers have, to come up with plausible erasures of the question mark. Most students, as you did, find the course esoteric, murky and impractical. The teachers, however, many of whom are mercifully unaware of the student reaction, have found sufficient justification for the course on various grounds which I think I can briefly summarize

Amalgamating Knowledge Bases, III - Algorithms, Data Structures, and Query Processing

Integrating knowledge from multiple sources is an important aspect of automated reasoning systems. In the first part of this series of papers, we presented a uniform declarative framework, based on annotated logics, for amalgamating multiple knowledge bases when these knowledge bases (possibly) contain inconsistencies, uncertainties, and non-monotonic modes of negation. We showed that annotated logics may be used, with some modifications, to mediate between different knowledge bases. The multiple knowledge bases are amalgamated by embedding the individual knowledge bases into a lattice. In this paper, we briefly describe an SLD-resolution based proof procedure that is sound and complete w.r.t. our declarative semantics. We will then develop an OLDT -resolution based query processing procedure, MULTI-OLDT , that satisfies two important properties: (1) efficient reuse of previous computations is achieved by maintaining a table -- we describe the structure of this table and show that table operations can be efficiently executed, and (2) approximate, interruptable query answering is achieved, i.e. it is possible to obtain an ``intermediate, approximate'' answer from the query processing procedure by interrupting it at any point in time during its execution. The design of the MULTI-OLDT procedure will include the development of run-time algorithms to incrementally and efficiently update the table. (Also cross-referenced as UMIACS-TR-94-35