Related papers: Modal logic approach to preferred bases in the qua…
The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for…
The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The…
Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
In probabilistic transition systems, behavioural metrics provide a more fine-grained and stable measure of system equivalence than crisp notions of bisimilarity. They correlate strongly to quantitative probabilistic logics, and in fact the…
This paper deals with the foundations of quantum mechanics. We start by outlining the characterisation, due to Birkhoff and Von Neumann, of the logical structures of the theories of classical physics and quantum mechanics, as boolean and…
It is shown that a coherent understanding of all quantized phenomena, including those governed by unitary evolution equations as well as those related to irreversible quantum measurements, can be achieved in a scenario of successive…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
We show that in a quantum measurement, the preferred basis is determined by the interaction between the apparatus and the quantum system, instead of by the environment. This interaction entangles three degrees of freedom, one system degree…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
The scientific methodology based on two descriptive levels, ontic (reality as it is ) and epistemic (observational), is briefly presented. Following Schr\"odinger, we point to the possible gap between these two descriptions. Our main aim is…
We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic…
The aim of this paper is to propose a many-valued modal framework to formalize reasoning with both graded preferences and propositions, in the style of van Benthem et al.'s classical modal logics for preferences. To do so, we start from Bou…
Quantum logic (QL) is a non-classical logic for analyzing the propositions of quantum physics. Modal logic MB, which is a logic that handles the value of the inner product that appears in quantum mechanics, was constructed with the…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
In this paper, epistemology and ontology of quantum states are discussed based on a completely new way of founding quantum theory. The fundamental notions are conceptual variables in the mind of an observer or in the joint minds of a group…