Related papers: Toward a More Natural Expression of Quantum Logic …
The (meta)logic underlying classical theory of computation is Boolean (two-valued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a logic of quantum mechanics more than sixty years ago. The major difference between Boolean…
According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
Quantum mechanics challenges classical intuitions of space, time, and causality via the superposition principle, which allows systems to exist in multiple states simultaneously. Niels Bohr addressed these paradoxes through his…
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of…
Quantum mechanics describes seemingly paradoxical relations between the outcomes of measurements that cannot be performed jointly. In Hilbert space, the outcomes of such incompatible measurements are represented by non-orthogonal states. In…
We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about…
We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…
The most peculiar, specifically quantum, features of quantum mechanics --- quantum nonlocality, indeterminism, interference of probabilities, quantization, wave function collapse during measurement --- are explained on a logical-geometrical…
In the paper the basic concepts of extended probability theory are introduced. The basic idea: the concept of an event as a subset of \Omega is replaced with the concept of an event as a partition. The partition is any set of disjoint…
Fully revealing the mathmatical structure of quantum contextuality is a significant task, while some known contextuality theories are only applicable for rank-1 projectors. That is because they adopt the observable-based definitions. This…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…