Continuous automata: bridging the gap between discrete and continuous time system models

The principled use of models in design and maintenance of a system is fundamental to the engineering methodology. As the complexity and sophistication of systems increase so do the demands on the system models required to design them. In particular the design of agent systems situated in the real world, such as robots, will require design models capable of expressing discrete and continuous changes of system parameters. Such systems are referred to as mode-switching or hybrid systems.This thesis investigates ways in which time is represented in automata system models with discretely and continuously changing parameters. Existing automaton approaches to hybrid modelling rely on describing continuous change at a sequence of points in time. In such approaches the time that elapses between each point is chosen non- deterministically in order to ensure that the model does not over-step a discrete change. In contrast, the new approach this thesis proposes describes continuous change by a continuum of points which can naturally and deterministically capture such change. As well as defining the semantics of individual models the nature of the temporal representation is particularly important in defining the composition of modular com­ponents. This new approach leads to a clear compositional semantics based on the synchronization of input and output values.The main contribution of this work is the derivation of a limiting process which provides a theoretical foundation for this new approach. It not only provides a link between dis­crete and continuous time representations, but also provides a basis for deciding which continuous time representations are theoretically sound. The resulting formalism, the Continuous I/O machine, is demonstrated to be comparable to Hybrid Automata in expressibility, but its representation of time gives it a much stronger compositional semantics based on the discrete synchronous machines from which it is derived.TThe conclusion of this work is that it is possible to define an automaton model that describes a continuum of events and that this can be effectively used to model complete mode-switching physical systems in a modular fashion

Proceedings of the Conference "sub8 - Sinn und Bedeutung" : 8th annual meeting of the Gesellschaft für Semantik

The volume is a collection of papers given at the conference “sub8 -- Sinn und Bedeutung”, the eighth annual conference of the Gesellschaft für Semantik, held at the Johann-Wolfgang-Goethe-Universität, Frankfurt (Germany) in September 2003. During this conference, experts presented ­ and discussed ­ various aspects of semantics. The very different topics included in this book provide insight into fields of ongoing Semantics research.Mit dem vorliegenden Band halten Sie eine Sammlung von Aufsätzen in Händen, die bei "Sinn und Bedeutung VIII", der Jahrestagung der "Gesellschaft für Semantik" in der Johann Wolfgang Goethe-Universität, Frankfurt/Main, im September 2003 vorgestellt worden sind. Die Beiträge umfassen verschiedenste Aspekte aktueller Semantik-Forschung und lassen sich inhaltlich den folgenden Kategorien zuordnen: (i) Semantik von Topic und Focus [Ebert / Endriss, Gyuris, Kaiser / Trueswell, Lee, Umbach, Wedgewood]; (ii) Semantik und Pragmatik von Fragen [Beck, Benz, Dekker]; (iii) Semantik von Tense und Voice [Fernando, Lekaku, Sailer]; (iv) Das Syntax-Semantik Interface [Kobuchi-Philip, Stateva, Zeijlstra], (v) Modalität [van Rooy, Copley] und (vi) Semantik [Aksan, Nicolas, Schäfer, Schlücker, Seong, Zwarts]

Meaning and the World

I motivate and develop a use-based semantic theory in opposition to the dominant paradigm in philosophical and linguistic semantics. Drawing inspiration from Wilfrid Sellars, I argue that contemporary semantic theories are faced with a basic problem of explanatory circularity. These theories universally presuppose that worldly knowledge of such things as properties or sets of possible worlds precedes and underlies knowledge of meaning. However, I argue that it is only through learning a language--mastering the rules governing the use of the expressions belonging to that language--that speakers can possibly have knowledge of the worldly entities appealed to by semanticists at the base level of their semantic theories. In response to this fundamental problem, I develop a formal semantic framework in which the meaning of a sentence is understood directly in terms of its role in discourse. In contrast to existing semantic frameworks, this framework does not presuppose speakers' worldly knowledge, and so is actually able to explain it. The result is not just a new kind of semantic theory, but a new conception of the relation between meaning and the world

On the trail of a thought : a kinenoetic analysis of problem-solving

The research in this thesis describes a microgenetic investigation of thought as it occurs in and through objects and informed by work in distributed cognition and interactivity. The thesis opens with a detailed survey of the arguments in cognitive philosophy around the ontological locus of cognition. I advance the conclusion that many of the open questions will not be solved by empirical methods and suggest a pragmatist approach. Four empirical studies are reported: Three laboratory-based studies which feature traditional problem-solving tasks found often in cognitive psychology and one which examines an artist solving problems which arise over the course of the artistic process. Each of the studies combines quantitative analysis with qualitative analysis of video recorded material to describe thinking in an open cognitive ecosystem. The first study reports performance on a word production task and finds that engagement with external representations is crucial to scaffold performance. The second study uses anagrams to assess the nature of that engagement and concludes a non-agentic model of mere luck is not sufficient. Study three examines performance on an insight problem and suggests that when the problem is not one which is easily scaffolded by material objects, systems form around other types of external scaffold. The final study tracks thought as it unfolds through making of a flower in an artist’s atelier. The findings of all the studies support the notion that cognition emerges in the form of material traces and actions on the world. The thesis introduces and develops two concepts—microserendipity and exaptative action—that offer a new perspective on the nature of problem solving and creativity. These concepts bring in sharp relief environmental chance in creativity when it is enacted; the methodology employed in the empirical work reported here also permits the identification of events when environmental chance is unnoticed. These phenomena operate outside the conscious observation of the problem solver so they cannot be tracked through traditional methods. The work reported here introduces kinenoetic analysis that trace in micro detail the dynamic transactional coupling between thought and objects that chart the origin of new ideas. The knowledge that the participant generates through the movement of objects mirrors the knowledge gained by the experimenter by these movements. The last chapter introduces kinemorphism as part of a qualitative description of the creative trajectory of an artist working with clay: form is unstable and arises out of action. Such a perspective suggests that what is produced cannot be explained by a reductive process that focuses on only one or the other, but rather must take into account the relationship which arises through action. Creativity from this perspective is transactional and relational. In terms of theoretical contributions, I cast doubt on an agent centric view of interactivity which posits an uncomplicated augmentative relationship between things beyond and within the brain and suggests instead a transactional approach to knowledge acquisition. These lead to novel observations on the role of the experiment in research in situated cognition. Reflections on the pluralistic method of kinenoetic analysis are offered and directions for future research are outlined

Algebraic properties of ordinary differential equations.

Thesis (Ph.D.)-University of Natal, 1995.In Chapter One the theoretical basis for infinitesimal transformations is presented with particular emphasis on the central theme of this thesis which is the invariance of ordinary differential equations, and their first integrals, under infinitesimal transformations. The differential operators associated with these infinitesimal transformations constitute an algebra under the operation of taking the Lie Bracket. Some of the major results of Lie's work are recalled. The way to use the generators of symmetries to reduce the order of a differential equation and/or to find its first integrals is explained. The chapter concludes with a summary of the state of the art in the mid-seventies just before the work described here was initiated. Chapter Two describes the growing awareness of the algebraic properties of the paradigms of differential equations. This essentially ad hoc period demonstrated that there was value in studying the Lie method of extended groups for finding first integrals and so solutions of equations and systems of equations. This value was emphasised by the application of the method to a class of nonautonomous anharmonic equations which did not belong to the then pantheon of paradigms. The generalised Emden-Fowler equation provided a route to major development in the area of the theory of the conditions for the linearisation of second order equations. This was in addition to its own interest. The stage was now set to establish broad theoretical results and retreat from the particularism of the seventies. Chapters Three and Four deal with the linearisation theorems for second order equations and the classification of intrinsically nonlinear equations according to their algebras. The rather meagre results for systems of second order equations are recorded. In the fifth chapter the investigation is extended to higher order equations for which there are some major departures away from the pattern established at the second order level and reinforced by the central role played by these equations in a world still dominated by Newton. The classification of third order equations by their algebras is presented, but it must be admitted that the story of higher order equations is still very much incomplete. In the sixth chapter the relationships between first integrals and their algebras is explored for both first order integrals and those of higher orders. Again the peculiar position of second order equations is revealed. In the seventh chapter the generalised Emden-Fowler equation is given a more modern and complete treatment. The final chapter looks at one of the fundamental algebras associated with ordinary differential equations, the three element 8£(2, R), which is found in all higher order equations of maximal symmetry, is a fundamental feature of the Pinney equation which has played so prominent a role in the study of nonautonomous Hamiltonian systems in Physics and is the signature of Ermakov systems and their generalisations