An Algorithmic Interpretation of Quantum Probability

The Everett (or relative-state, or many-worlds) interpretation of quantum mechanics has come under fire for inadequately dealing with the Born rule (the formula for calculating quantum probabilities). Numerous attempts have been made to derive this rule from the perspective of observers within the quantum wavefunction. These are not really analytic proofs, but are rather attempts to derive the Born rule as a synthetic a priori necessity, given the nature of human observers (a fact not fully appreciated even by all of those who have attempted such proofs). I show why existing attempts are unsuccessful or only partly successful, and postulate that Solomonoff's algorithmic approach to the interpretation of probability theory could clarify the problems with these approaches. The Sleeping Beauty probability puzzle is used as a springboard from which to deduce an objectivist, yet synthetic a priori framework for quantum probabilities, that properly frames the role of self-location and self-selection (anthropic) principles in probability theory. I call this framework "algorithmic synthetic unity" (or ASU). I offer no new formal proof of the Born rule, largely because I feel that existing proofs (particularly that of Gleason) are already adequate, and as close to being a formal proof as one should expect or want. Gleason's one unjustified assumption--known as noncontextuality--is, I will argue, completely benign when considered within the algorithmic framework that I propose. I will also argue that, to the extent the Born rule can be derived within ASU, there is no reason to suppose that we could not also derive all the other fundamental postulates of quantum theory, as well. There is nothing special here about the Born rule, and I suggest that a completely successful Born rule proof might only be possible once all the other postulates become part of the derivation. As a start towards this end, I show how we can already derive the essential content of the fundamental postulates of quantum mechanics, at least in outline, and especially if we allow some educated and well-motivated guesswork along the way. The result is some steps towards a coherent and consistent algorithmic interpretation of quantum mechanics

Hybrid Cloud Model Checking Using the Interaction Layer of HARMS for Ambient Intelligent Systems

Soon, humans will be co-living and taking advantage of the help of multi-agent systems in a broader way than the present. Such systems will involve machines or devices of any variety, including robots. These kind of solutions will adapt to the special needs of each individual. However, to the concern of this research effort, systems like the ones mentioned above might encounter situations that will not be seen before execution time. It is understood that there are two possible outcomes that could materialize; either keep working without corrective measures, which could lead to an entirely different end or completely stop working. Both results should be avoided, specially in cases where the end user will depend on a high level guidance provided by the system, such as in ambient intelligence applications. This dissertation worked towards two specific goals. First, to assure that the system will always work, independently of which of the agents performs the different tasks needed to accomplish a bigger objective. Second, to provide initial steps towards autonomous survivable systems which can change their future actions in order to achieve the original final goals. Therefore, the use of the third layer of the HARMS model was proposed to insure the indistinguishability of the actors accomplishing each task and sub-task without regard of the intrinsic complexity of the activity. Additionally, a framework was proposed using model checking methodology during run-time for providing possible solutions to issues encountered in execution time, as a part of the survivability feature of the systems final goals

Revisiting the Applicability of Metaphysical Identity in Quantum Mechanics

We discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the semantic level, has severe difficulties when considering the syntactic level of the theory

The will and its freedom in the thought of Plato, Aristotle, Augustine, and Kant

Thesis (Ph.D.)--Boston University.1. Problem. The problem of this dissertation is to examine the doctrines of the will in the thought of Plato; Aristotle, Augustine, and Kant and to relate their conceptions of freedom to their doctrines of the will. 2. Method. The method consists in examining primary sources which define and interpret the will and its freedom. [TRUNCATED

Holmes and Laski on natural law

Thesis (Ph.D.)--Boston University.Using the two volumes of the Helmes-Laski Correspondence, published by Harvard and edited by Mark DeWolfe Howe, as one of its principal sources, this dissertation examines the circumstances leading up to the publication of Justice Oliver Wendell Holmes' essay, Natural Law in the Harvard Law Review in November, 1918, when Harold J. Laski was its editor. From this focus several lines of inquiry expand, developing from the two major questions of the dissertation: 1) What is Natural Law? and 2) How significant, profound and pertinent were Holmes' and Laski's contribution to the theory of Natural Law, the validity of which they denied? A last chapter examines the co-fusions in Laski's connecting together the plural sovereignty with the personality of associations theories -- ideas he apparently gathered from Otto Gierke. Gierke's position is analyzed directly from his writings, with the conclusion that he was unclear in his own formulations, and that Laski was even more unclear in what he thought Gierke said. Reasons for the vitiation of Laski's work are analyzed, and in summary his frustrations are stressed, while Holmes' great accomplishment within the framework of his own creative inconsistencies is forcefully stated. The conclusion of the whole is that no matter what they said they believed both Holmes and Laski lived and worked as though they believed in Natural Law

Adaptive music: Automated music composition and distribution

Creativity, or the ability to produce new useful ideas, is commonly associated to the human being; but there are many other examples in nature where this phenomenon can be observed. Inspired by this fact, in engineering, and particularly in computational sciences, many different models have been developed to tackle a number of problems. Music, a form of art broadly present along the human history, is the main field addressed in this thesis, taking advantage of the kind of ideas that bring diversity and creativity to nature and computation. We present Melomics, an algorithmic composition method based on evolutionary search, with a genetic encoding of the solutions, which are interpreted in a complex developmental process that leads to music in the standard formats. This bioinspired compositional system has exhibited a high creative power and versatility to produce music of different type, which in many occasions has proven to be indistinguishable from the music made by human composers. The system also has enabled the emergence of a set of completely novel applications: from effective tools to help anyone to easily obtain the precise music they need, to radically new uses like adaptive music for therapy, amusement or many other purposes. It is clear to us that there is much research work yet to do in this field; and that countless and new unimaginable uses will derive from it

Model and Proof Theory of Constructive ALC, Constructive Description Logics

Description logics (DLs) represent a widely studied logical formalism with a significant impact in the field of knowledge representation and the Semantic Web. However, they are equipped with a classical descriptive semantics that is characterised by a platonic notion of truth, being insufficiently expressive to deal with evolving and incomplete information, as from data streams or ongoing processes. Such partially determined and incomplete knowledge can be expressed by relying on a constructive semantics. This thesis investigates the model and proof theory of a constructive variant of the basic description logic ALC, called cALC. The semantic dimension of constructive DLs is investigated by replacing the classical binary truth interpretation of ALC with a constructive notion of truth. This semantic characterisation is crucial to represent applications with partial information adequately, and to achieve both consistency under abstraction as well as robustness under refinement, and on the other hand is compatible with the Curry-Howard isomorphism in order to form the cornerstone for a DL-based type theory. The proof theory of cALC is investigated by giving a sound and complete Hilbert-style axiomatisation, a Gentzen-style sequent calculus and a labelled tableau calculus showing finite model property and decidability. Moreover, cALC can be strengthened towards normal intuitionistic modal logics and classical ALC in terms of sound and complete extensions and hereby forms a starting point for the systematic investigation of a constructive correspondence theory.Beschreibungslogiken (BLen) stellen einen vieluntersuchten logischen Formalismus dar, der den Bereich der Wissensrepräsentation und das Semantic Web signifikant geprägt hat. Allerdings basieren BLen meist auf einer klassischen deskriptiven Semantik, die gekennzeichnet ist durch einen idealisierten Wahrheitsbegriff nach Platons Ideenlehre, weshalb diese unzureichend ausdrucksstark sind, um in Entwicklung befindliches und unvollständiges Wissen zu repräsentieren, wie es beispielsweise durch Datenströme oder fortlaufende Prozesse generiert wird. Derartiges partiell festgelegtes und unvollständiges Wissen lässt sich auf der Basis einer konstruktiven Semantik ausdrücken. Diese Arbeit untersucht die Model- und Beweistheorie einer konstruktiven Variante der Basis-BL ALC, die im Folgenden als cALC bezeichnet wird. Die Semantik dieser konstruktiven Beschreibungslogik resultiert daraus, die traditionelle zweiwertige Interpretation logischer Aussagen des Systems ALC durch einen konstruktiven Wahrheitsbegriff zu ersetzen. Eine derartige Interpretation ist die Voraussetzung dafür, um einerseits Anwendungen mit partiellem Wissen angemessen zu repräsentieren, und sowohl die Konsistenz logischer Aussagen unter Abstraktion als auch ihre Robustheit unter Verfeinerung zu gewährleisten, und andererseits um den Grundstein für eine Beschreibungslogik-basierte Typentheorie gemäß dem Curry-Howard Isomorphismus zu legen. Die Ergebnisse der Untersuchung der Beweistheorie von cALC umfassen eine vollständige und korrekte Hilbert Axiomatisierung, einen Gentzen Sequenzenkalkül, und ein semantisches Tableaukalkül, sowie Beweise zur endlichen Modelleigenschaft und Entscheidbarkeit. Darüber hinaus kann cALC zu normaler intuitionistischer Modallogik und klassischem ALC durch vollständige und korrekte Erweiterungen ausgebaut werden, und bildet damit einen Startpunkt für die systematische Untersuchung einer konstruktiven Korrespondenztheorie