Related papers: Theory of processes
Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in…
We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
Subject of present paper is the review of results of authors on foliation theory and applications of foliation theory in control systems. The paper consists of two parts. In the first part the results of authors on foliation theory are…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…
Our approach is basically a coherence approach, but we avoid the well-known pitfalls of coherence theories of truth. Consistency is replaced by reliability, which expresses support and attack, and, in principle, every theory (or agent,…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
The main subjects of this text are: (1) Generalization of concepts and operations, like distance and size, to situations where they are not definable in the usual way. (2) A pragmatic theory of handling contradictions using reliability of…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
The general translator formalism and computing specific implementations are proposed. The implementation of specific elements necessary to process the source and destination information within the translators are presented. Some common…
This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed…
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…
A universal process of a process calculus is one that, given the G\"{o}del index of a process of a certain type, produces a process equivalent to the encoded process. This paper demonstrates how universal processes can be formally defined…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
Software engineering concepts and processes are worthy of formal study; and yet we seldom formalize them. This "research ideas" article explores what a theory of software engineering could and should look like. Software engineering research…
This chapter provides an introduction to some basic concepts of epistemic logic, basic formal languages, their semantics, and proof systems. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…