Related papers: Atomism Axiomatised Using Mereological Composition…

In a series of papers in the last ten years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations…

We introduce an atomic formula intuitively saying that given variables are independent from given other variables if a third set of variables is kept constant. We contrast this with dependence logic. We show that our independence atom gives…

Microscopic nuclear theory is based on the tenet that atomic nuclei can be accurately described as collections of point-like nucleons interacting via two- and many-body forces obeying nonrelativistic quantum mechanics -- and the concept of…

A relation algebra is called measurable when its identity is the sum of measurable atoms, and an atom is called measurable if its square is the sum of functional elements. In this paper we show that atomic measurable relation algebras have…

We combine the language of monoids with the language of preorders so as to refine some fundamental aspects of the classical theory of factorization and prove an abstract factorization theorem with a variety of applications. In particular,…

We analyze von Weizs\"acker view regarding the concept of information in physics. In his view, information arises from the reduction of properties of a physical object to their logical descriptive propositions. The smallest element of a…

Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…

We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…

I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements)…

The present essay provides a new metaphysical interpretation of Relational Quantum Mechanics (RQM) in terms of mereological bundle theory. The essential idea is to claim that a physical system in RQM can be defined as a mereological fusion…

Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is…

Humans have the innate capability to answer diverse questions, which is rooted in the natural ability to correlate different concepts based on their semantic relationships and decompose difficult problems into sub-tasks. On the contrary,…

Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very…

Life continuously changes its own components and states at each moment through interaction with the external world, while maintaining its own individuality in a cyclical manner. Such a property, known as "autonomy," has been formulated…

Motivated by a revision of the classical equations of electromagnetism that allow for the inclusion of solitary waves in the solution space, the material collected in these notes examines the consequences of adopting the modified model in…

We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a…

Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical phenomena, but they also constitute our fundamental assumptions about reality. Many of the…

Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of…

An (additive) commutative monoid is called atomic if every given non-invertible element can be written as a sum of atoms (i.e., irreducible elements), in which case, such a sum is called a factorization of the given element. The number of…

Let $M$ be a cancellative and commutative monoid. A non-invertible element of $M$ is called an atom (or irreducible element) if it cannot be factored into two non-invertible elements, while an atom $a$ of $M$ is called strong if $a^n$ has a…