Being and Change: Foundations of a Realistic Operational Formalism

The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity of a more abstract nature, for example a concept, or a cultural artifact, or the mind of a person, etc..., which means that we aim at very general description. The effect that a context has on the state of the entity plays a fundamental role, which means that our approach is intrinsically contextual. The approach is inspired by the mathematical formalisms that have been developed in axiomatic quantum mechanics, where a specific type of quantum contextuality is modelled. However, because in general states also influence context -- which is not the case in quantum mechanics -- we need a more general setting than the one used there. Our focus on context as a fundamental concept makes it possible to unify `dynamical change' and `change under influence of measurement', which makes our approach also more general and more powerful than the traditional quantum axiomatic approaches. For this reason an experiment (or measurement) is introduced as a specific kind of context. Mathematically we introduce a state context property system as the structure to describe an entity by means of its states, contexts and properties. We also strive from the start to a categorical setting and derive the morphisms between state context property systems from a merological covariance principle. We introduce the category SCOP with as elements the state context property systems and as morphisms the ones that we derived from this merological covariance principle. We introduce property completeness and state completeness and study the operational foundation of the formalismComment: 44 page

Reality and Probability: Introducing a New Type of Probability Calculus

We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty. If we consider a conception of reality where probability plays a fundamental role it can be shown that standard probability theory is not well suited to substitute 'certainty' by means of 'probability equal to 1'. The analysis of this problem leads us to propose a new type of probability theory that is a generalization of standard probability theory. This new type of probability is a function to the set of all subsets of the interval [0, 1] instead of to the interval [0, 1] itself, and hence its evaluation happens by means of a subset instead of a number. This subset corresponds to the different limits of sequences of relative frequency that can arise when an intrinsic lack of knowledge about the context and how it influences the state of the physical entity under study in the process of experimentation is taken into account. The new probability theory makes it possible to define probability on the whole set of experiments within the Geneva-Brussels approach to quantum mechanics, which was not possible with standard probability theory. We introduce the structure of a 'state experiment probability system' and derive the state property system as a special case of this structure. The category SEP of state experiment probability systems and their morphisms is linked with the category SP of state property systems and their morphismsComment: 27 page

Electric/magnetic reciprocity in premetric electrodynamics with and without magnetic charge, and the complex electromagnetic field

We extend an axiomatic approach to classical electrodynamics, which we developed recently, to the case of non-vanishing magnetic charge. Then two axioms, namely those of the existence of the Lorentz force (Axiom 2) and of magnetic flux conservation (Axiom 3) have to be generalized. Electric/magnetic reciprocity constitutes a guiding principle for this undertaking. The extension of the axioms can be implemented at a premetric stage, i.e., when metric and connection of spacetime don't play a role. Complex Riemann-Silberstein fields of the form $(E\pm i {\cal H},{\cal D}\pm i B)$ have a natural place in the theory, independent of the Hodge duality mapping defined by any particular metric.Comment: 13 pages in latex, 3 references added, text slightly revise

Failure of interpolation in the intuitionistic logic of constant domains

This paper shows that the interpolation theorem fails in the intuitionistic logic of constant domains. This result refutes two previously published claims that the interpolation property holds.Comment: 13 pages, 0 figures. Overlaps with arXiv 1202.1195 removed, the text thouroughly reworked in terms of notation and style, historical notes as well as some other minor details adde

Failure of interpolation in the intuitionistic logic of constant domains

This paper shows that the interpolation theorem fails in the intuitionistic logic of constant domains. This result refutes two previously published claims that the interpolation property holds.Comment: 13 pages, 0 figures. Overlaps with arXiv 1202.1195 removed, the text thouroughly reworked in terms of notation and style, historical notes as well as some other minor details adde