Related papers: The harmony, reflection and other principles of co…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.
The theory of causal fermion systems is an approach to describe fundamental physics. We here introduce the mathematical framework and give an overview of the objectives and current results.
This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at…
It is widely claimed that the natural axiom systems$\unicode{x2013}$including the large cardinal axioms$\unicode{x2013}$form a well-ordered hierarchy. Yet, as is well-known, it is possible to exhibit non-linearity and ill-foundedness by…
A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
Physicists study a wide variety of phenomena creating new interdisciplinary research fields by applying theories and methods originally developed in physics in order to solve problems in economics, social science, biology, medicine,…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different…
The problem of "what is 'system'?" is in the very foundations of modern quantum mechanics. Here, we point out the interest in this topic in the information-theoretic context. E.g., we point out the possibility to manipulate a pair of…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
This textbook introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…
Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative…