Related papers: An algebraic framework for information theory: Cla…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
In this paper we derive the complex Hilbert space formalism of quantum theory from four simple information theoretic axioms. It is shown that quantum theory is the only non classical probabilistic theory satisfying the following axioms:…
In our previous arXiv papers ("The Information and the Matter", v1, v5; more systematically the informational conception is presented in the paper "The Information as Absolute", 2010) it was rigorously shown that Matter in our Universe -…
This work is a discussion on the concept of information. We define here information as an abstraction that is able to be copied. We consider the connection between the process of copying information in quantum systems and the emergence of…
Statistical hypothesis testing is the central method to demarcate scientific theories in both exploratory and inferential analyses. However, whether this method befits such purpose remains a matter of debate. Established approaches to…
We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…
When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…
Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
A significant part of human activity today consists of searching for a piece of information online, utilizing knowledge repositories. This endeavor may be time-consuming if the individual searching for the information is unfamiliar with the…
We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution,…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
One of the greatest research challenges of this century is to understand the neural basis for how behavior emerges in brain-body-environment systems. To this end, research has flourished along several directions but have predominantly…
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
The information-spectrum analysis made by Han for classical hypothesis testing for simple hypotheses is extended to a unifying framework including both classical and quantum hypothesis testing as well as fixed-length source coding, whereby…