A methodology for the selection of a paradigm of reasoning under uncertainty in expert system development

The aim of this thesis is to develop a methodology for the selection of a paradigm of reasoning under uncertainty for the expert system developer. This is important since practical information on how to select a paradigm of reasoning under uncertainty is not generally available. The thesis explores the role of uncertainty in an expert system and considers the process of reasoning under uncertainty. The possible sources of uncertainty are investigated and prove to be crucial to some aspects of the methodology. A variety of Uncertainty Management Techniques (UMTs) are considered, including numeric, symbolic and hybrid methods. Considerably more information is found in the literature on numeric methods, than the latter two. Methods that have been proposed for comparing UMTs are studied and comparisons reported in the literature are summarised. Again this concentrates on numeric methods, since there is more literature available. The requirements of a methodology for the selection of a UMT are considered. A manual approach to the selection process is developed. The possibility of extending the boundaries of knowledge stored in the expert system by including meta-data to describe the handling of uncertainty in an expert system is then considered. This is followed by suggestions taken from the literature for automating the process of selection. Finally consideration is given to whether the objectives of the research have been met and recommendations are made for the next stage in researching a methodology for the selection of a paradigm of reasoning under uncertainty in expert system development

Death of Paradox: The Killer Logic Beneath the Standards of Proof

The prevailing but contested view of proof standards is that factfinders should determine facts by probabilistic reasoning. Given imperfect evidence, they should ask themselves what they think the chances are that the burdened party would be right if the truth were to become known; they then compare those chances to the applicable standard of proof. I contend that for understanding the standards of proof, the modern versions of logic — in particular, fuzzy logic and belief functions — work better than classical probability. This modern logic suggests that factfinders view evidence of an imprecisely perceived and described reality to form a fuzzy degree of belief in a fact’s existence; they then apply the standard of proof in accordance with the theory of belief functions, by comparing their belief in a fact’s existence to their belief in its negation. This understanding explains how the standard of proof actually works in the law world. It gives a superior mental image of the factfinders’ task, conforms more closely to what we know of people’s cognition, and captures better what the law says its standards are and how it manipulates them. One virtue of this conceptualization is that it is not a radically new view. Another virtue is that it nevertheless manages to resolve some stubborn problems of proof, including the infamous conjunction paradox

Multivalued Logic, Neutrosophy and Schrodinger equation

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by observation that despite almost eight decades, there is indication that some of those paradoxes known in Quantum Physics are not yet solved. In our knowledge, this is because the solution of those paradoxes requires re-examination of the foundations of logic itself, in particular on the notion of identity and multi-valuedness of entity. The book is also intended for young physicist fellows who think that somewhere there should be a ‘complete’ explanation of these paradoxes in Quantum Mechanics. If this book doesn’t answer all of their questions, it is our hope that at least it offers a new alternative viewpoint for these old questions

A Dempster-Shafer theory inspired logic.

Issues of formalising and interpreting epistemic uncertainty have always played a prominent role in Artificial Intelligence. The Dempster-Shafer (DS) theory of partial beliefs is one of the most-well known formalisms to address the partial knowledge. Similarly to the DS theory, which is a generalisation of the classical probability theory, fuzzy logic provides an alternative reasoning apparatus as compared to Boolean logic. Both theories are featured prominently within the Artificial Intelligence domain, but the unified framework accounting for all the aspects of imprecise knowledge is yet to be developed. Fuzzy logic apparatus is often used for reasoning based on vague information, and the beliefs are often processed with the aid of Boolean logic. The situation clearly calls for the development of a logic formalism targeted specifically for the needs of the theory of beliefs. Several frameworks exist based on interpreting epistemic uncertainty through an appropriately defined modal operator. There is an epistemic problem with this kind of frameworks: while addressing uncertain information, they also allow for non-constructive proofs, and in this sense the number of true statements within these frameworks is too large. In this work, it is argued that an inferential apparatus for the theory of beliefs should follow premises of Brouwer's intuitionism. A logic refuting tertium non daturìs constructed by defining a correspondence between the support functions representing beliefs in the DS theory and semantic models based on intuitionistic Kripke models with weighted nodes. Without addional constraints on the semantic models and without modal operators, the constructed logic is equivalent to the minimal intuitionistic logic. A number of possible constraints is considered resulting in additional axioms and making the proposed logic intermediate. Further analysis of the properties of the created framework shows that the approach preserves the Dempster-Shafer belief assignments and thus expresses modality through the belief assignments of the formulae within the developed logic

An outline theory of art on cybernetic principles

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The object of this study is to draw art into the common net of organization, along with those other enterprizes more commonly associated with the exercise of intelligence. The method chosen for this is based upon the idea of effective procedures, namely by setting out to construct a (notional) 'art machine'. The argument falls into two parts, the first dealing with the general concept of authorship and the second with its products. Part I offers a definition of an abstract, rudimentary productive process and describes its observers. There is an examination of the relation between structure and purpose, which moves towards a general definition of authorship made in terms of extracting order from a surrounding. Principles of order extraction are examined, with particular reference to the Law of Requisite Variety. Examination of extracted order, as structure, heuristics and the like, leads to discussion of the transmission of purposes between purposeful systems, as well as general problems of constraint, and of regulation and control. Part I ends with a proposal for a paradigm for a rudimentary mechanical author. Part II concentrates on the products of authorship, seeking characterizing features of those that may be classified as art. There is discussion of objective knowledge and its value and of the characteristics of experience as a form of objective knowledge. It is suggested that art is concerned with experience and that this dictates its method, which is to produce simulation procedures based on a language constituted by the synthetic structures discussed in Part I. Lines are suggested for realizing an 'art machine' and there is a review of prospects. A section of notes consisting of speculative ideas and empirical applications connected with the conclusions of the text follows Part II

Approximate truth and causal strength in science.

In Chapter One I motivate the search for an account of approximate truth as being the way to make sense of how our best scientific theories are simultaneously false but useful, and of how the same theory (even a true one) varies in its usefulness depending on context. I evaluate existing approaches and find that they fail - among other reasons - because they are unable to accommodate how two errors of similar logical seriousness nevertheless may have greatly different implications for approximate truth. The only way round this is some form of weighting scheme across logical statements that is motivated by extra-logical criteria. The little existing work along these lines suffers from insufficient generality, and I suggest instead a weighting scheme based on the notion of causal strength. In Chapter Two I develop the details of following such a prescription. It turns out to be crucial to highlight a hitherto underappreciated dichotomy between what I label the 'ontological' and 'empirical' senses of approximate truth. After outlining the practical advantages of my approach I discuss a number of technicalities, including several that confound all previous approaches. (I also outline an exact formal definition in an appendix.) Finally, I tackle the vexed issue of comparing two models with incommensurable ontologies. One of the results of the complicated discussion is that no sense can be made of science in general getting nearer the truth, only sense made of particular models getting nearer the truth of particular explananda. In Chapter Three I flesh out the notion - key for my scheme - of causal strength, giving a formal definition and sorting through the numerous necessary technicalities. I also explain how straightforward sense can be made of causal strengths even in cases of interactive effects and also even in cases where two causes are apparently incommensurable

Mapa de la recerca del Campus de Vilanova i la Geltrú

Postprint (author’s final draft