Algebraic Stream Processing

We identify and analyse the typically higher-order approaches to stream processing in the literature. From this analysis we motivate an alternative approach to the specification of SPSs as STs based on an essentially first-order equational representation. This technique is called Cartesian form specification. More specifically, while STs are properly second-order objects we show that using Cartesian forms, the second-order models needed to formalise STs are so weak that we may use and develop well-understood first-order methods from computability theory and mathematical logic to reason about their properties. Indeed, we show that by specifying STs equationally in Cartesian form as primitive recursive functions we have the basis of a new, general purpose and mathematically sound theory of stream processing that emphasises the formal specification and formal verification of STs. The main topics that we address in the development of this theory are as follows. We present a theoretically well-founded general purpose stream processing language ASTRAL (Algebraic Stream TRAnsformer Language) that supports the use of modular specification techniques for full second-order STs. We show how ASTRAL specifications can be given a Cartesian form semantics using the language PREQ that is an equational characterisation of the primitive recursive functions. In more detail, we show that by compiling ASTRAL specifications into an equivalent Cartesian form in PREQ we can use first-order equational logic with induction as a logical calculus to reason about STs. In particular, using this calculus we identify a syntactic class of correctness statements for which the verification of ASTRAL programmes is decidable relative to this calculus. We define an effective algorithm based on term re-writing techniques to implement this calculus and hence to automatically verify a very broad class of STs including conventional hardware devices. Finally, we analyse the properties of this abstract algorithm as a proof assistant and discuss various techniques that have been adopted to develop software tools based on this algorithm

Encoding logical theories of programs

Nowadays, in many critical situations (such as on-board software), it is manda-tory to certify programs and systems, that is, to prove formally that they meet their specifications. To this end, many logics and formal systems have been proposed for rea-soning rigorously on properties of programs and systems. Their usage on non-trivial cases, however, is often cumbersome and error-prone; hence, a computerized proof assistant is required. This thesis is a contribution to the field of computer-aided formal reasoning. In recent years, Logical Frameworks (LF's) have been proposed as general metalan-guages for the description (encoding) of formal systems. LF's streamline the implementa-tion of proof systems on a machine; moreover, they allow for conceptual clarification of the object logics. The encoding methodology of LF's (based on the judgement as types, proofs as \u3bb-terms paradigm) has been successfully applied to many logics; however, the encoding of the many peculiarities presented by formal systems for program logics is problematic. In this thesis we propose a general methodology for adequately encoding formal systems for reasoning on programs. We consider Structured and Natural Operational Semantics, Modal Logics, Dynamic Logics, and the \ub5-calculus. Each of these systems presents distinc-tive problematic features; in each case, we propose, discuss and prove correct, alternative solutions. In many cases, we introduce new presentations of these systems, in Natural Deduction style, which are suggested by the metalogical analysis induced by the method-ology. At the metalogical level, we generalize and combine the concept of consequence relation by Avron and Aczel, in order to handle schematic and multiple consequences. We focus on a particular Logical Framework, namely the Calculus of Inductive Con-structions, originated by Coquand and Huet, and its implementation, Coq. Our inves-tigation shows that this framework is particularly flexible and suited for reasoning on properties of programs and systems. Our work could serve as a guide and reference to future users of Logical Frameworks

Micro-intelligence for the IoT: logic-based models and technologies

Computing is moving towards pervasive, ubiquitous environments in which devices, software agents and services are all expected to seamlessly integrate and cooperate in support of human objectives. An important next step for pervasive computing is the integration of intelligent agents that employ knowledge and reasoning to understand the local context and share this information in support of intelligent applications and interfaces. Such scenarios, characterised by "computation everywhere around us", require on the one hand software components with intelligent behaviour in terms of objectives and context, and on the other their integration so as to produce social intelligence. Logic Programming (LP) has been recognised as a natural paradigm for addressing the needs of distributed intelligence. Yet, the development of novel architectures, in particular in the context Internet of Things (IoT), and the emergence of new domains and potential applications, are creating new research opportunities where LP could be exploited, when suitably coupled with agent technologies and methods so that it can fully develop its potential in the new context. In particular, the LP and its extensions can act as micro-intelligence sources for the IoT world, both at the individual and the social level, provided that they are reconsidered in a renewed architectural vision. Such micro-intelligence sources could deal with the local knowledge of the devices taking into account the domain specificity of each environment. The goal of this thesis is to re-contextualise LP and its extensions in these new domains as a source of micro-intelligence for the IoT world, envisioning a large number of small computational units distributed and situated in the environment, thus promoting the local exploitation of symbolic languages with inference capabilities. The topic is explored in depth and the effectiveness of novel LP models and architectures -and of the corresponding technology- expressing the concept of micro-intelligence is tested

A framework for assistive communications technology in cross-cultural healthcare

Rural and remote Australian Aboriginal communities suffer seriously adverse life expectancy rates, lifestyle disease complications and hospital treatment needs due to type 2 diabetes. In great part this is due to communications barriers arising from the lack of equitable acculturation within patient-practitioner consultations. This research presents a framework foundation for a computerised patient-practitioner lingua franca. Behavioural and design science ontology development delivers an intercultural patient-practitioner type 2 diabetes assistive communications system, known as P-PAC

The religious and theological foundations of natural science

This thesis examines the religions and theological foundations of natural science. A mythology has arisen, both popularly and academieally, that locates the historical origins of science in the great humanistic movements of the Renaissance and Eniightenment. Conversely Calvinism and Puritenism are regarded as regressive forces, the enemies of freedom and progress, interested only in rigerons morality and otherwordly piety. Philosophically there is a wide spread divorce between faith and knowledge, religion and science, while sociologically science is seen to advance with the shaking off of the fetters of religious belief. The choice of approach was difficult. I elected for an overview rather than an exhaustive detail of one aspect. This was a choice against specialisation and the abstreative loss of concrete reality. It alse seems more consonant with the topic under consideration. The major divisions are as follows: Part I: An historical section which contextualises the study and indicates origins and motivations of modern science in religious interests - particularly Calvinism. By the nature of such a study there is a degree of ambivalence. Part II: The thesis is established by a review and brief eritique of secular philosophies of sciences. This again is ambivalent though I have scught to plant signposts to the clearer statement presented in Part IV. Part III: A survey of Christian responses to the topic. While remaining within Protestant thought I have tried to do justice to as many divergent positions as is consistent with overall coherence. Part IV: this seeks to establish the religious and theological foundations of natural science on Christian perspectival grounds - viewing religion as the crientation of the heart in a basic commitment to the universe: and seeing in the theology of the sovereignty of God, His law, the dectrines of creation and cultural activity, clear motivations to scientific activity. So this is the crux of my thesis. I also give some practical application in terms of the problems of the environment and technic, and how the fundamental issues pertain therein. I believe the basic contribution to the subject is not, in the first instance, detailed originality but in an original synthesis of materil. Detailed contributions are inter alia: 1. A critical introduction to the thought of 'Cosmonomiem' where that impinges on my topic. The study, based within the parameters of nesyeweerd's 'Cosmonomic Idea', seeks to apply cosmonomism in a more scientific field than that in which most of its proponents work. 2. More specifically I point to my suggested solution of Mackay's complementary model of science and relgions; 3. My causal-perspectival interpretation of the influence of Calvin(ism) which goes further than Merton, Neekyaas or Torrance. 4. My critique of the theological spectrum - liberal and evangelical. I point particularly to my analysis of erangelicals who are largely uncritiqued from within their own perspective and ignored by liberals, despite their vest amount of literature on science and belief; and 5. The exposure of a confusion between 'science' and 'scientia' ; and between 'religion', 'theology' and 'faith'. Inter alia my conclusions include: 1. Religion and natural science (but not theology and natural science) are not separate entities, for the former founds and activates the latter. The whole discussion of science 'and' religion/belief is a false dichotomy and therefore a pseudo-problem. 2. The religious foundation of science does not dictate/coereo scientific scientific theories. While it can give a definite 'no' to some theories, it can only give a conditional 'yes' to theories. 3. There is, strictly speaking, no 'theology of science' but a theological framework within which science can be understood. 4. Unnecessary conceptual problems have been created by seeing laws of nature as antonomous from the law of God. 5. 'The' scientific method is mythological