10 found
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  1. Quasi-set theory: a formal approach to a quantum ontology of properties.Federico Holik, Juan Pablo Jorge, Décio Krause & Olimpia Lombardi - 2022 - Synthese 200 (5):1-26.
    In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate meta-language to speak of the proposed ontology of properties and its structure.
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  2.  73
    Sobre una teoría ‘pura’ de casi-conjuntos y su aplicación a una ontología cuántica de propiedades.Décio Krause & Juan Pablo Jorge - manuscript
    In this paper, we introduce a quasi-set theory without atoms. The quasi-sets (qsets) can have as elements completely indiscernible things which do not turn out to be the very same thing as it would be implied if its underlying logic was classical logic. A quasi-set can have a cardinal, called its quasi-cardinal, but this is made so that, at least for the finite case, the quasi-cardinal is not an ordinal, and hence the indistinguishable elements of a quasi-set cannot be ordered. (...)
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  3.  52
    Non-Deterministic Semantics for Quantum States.Juan Pablo Jorge & Federico Holik - 2020 - Entropy 22 (2):156.
    In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based (...)
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  4.  50
    Lógica cuántica, Nmatrices y adecuación, II.Juan Pablo Jorge & Federico Holik - 2023 - Teorema: International Journal of Philosophy 42 (1):149-169.
    By elaborating on the results presented in Lógica cuántica, Nmatrices y adecuación I, here we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics based on Nmatrices. We present a proof of the impossibility of providing a functional semantics for the quantum lattice. An advantage of our proof is that it is independent of the number of truth values involved, generalizing previous works. Due to the impossibility of defining adequate (...)
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  5. An Approach to QST-based Nmatrices Semantics.Juan Pablo Jorge, Federico Holik & Décio Krause - 2023 - Principia: An International Journal of Epistemology 27 (3):539-607.
    This paper introduces the theory QST of quasets as a formal basis for the Nmatrices. The main aim is to construct a system of Nmatrices by substituting standard sets by quasets. Since QST is a conservative extension of ZFA (the Zermelo-Fraenkel set theory with Atoms), it is possible to obtain generalized Nmatrices (Q-Nmatrices). Since the original formulation of QST is not completely adequate for the developments we advance here, some possible amendments to the theory are also considered. One of the (...)
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  6. Open Problems in the Development of a Quantum Mereology.Federico Holik & Juan Pablo Jorge - 2023 - In Jonas R. B. Arenhart & Raoni W. Arroyo (eds.), Non-Reflexive Logics, Non-Individuals, and the Philosophy of Quantum Mechanics: Essays in Honour of the Philosophy of Décio Krause. Springer Verlag. pp. 157-176.
    Mereology deals with the study of the relations between wholes and parts. In this work we will discuss different developments and open problems related to the formulation of a quantum mereology. In particular, we will discuss different advances in the development of formal systems aimed to describe the whole-parts relationship in the context of quantum theory.
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  7.  91
    Mathematical Models for Unstable Quantum Systems and Gamow States.Manuel Gadella, Sebastian Fortin, Juan Pablo Jorge & Marcelo Losada - 2022 - Entropy 24 (6):804.
    We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of (...)
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  8.  61
    An Algebraic Model for Quantum Unstable States.Sebastian Fortin, Manuel Gadella, Federico Holik, Juan Pablo Jorge & Marcelo Losada - 2022 - Mathematics 10 (23).
    In this review, we present a rigorous construction of an algebraic method for quantum unstable states, also called Gamow states. A traditional picture associates these states to vectors states called Gamow vectors. However, this has some difficulties. In particular, there is no consistent definition of mean values of observables on Gamow vectors. In this work, we present Gamow states as functionals on algebras in a consistent way. We show that Gamow states are not pure states, in spite of their representation (...)
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  9. Lógica cuántica, Nmatrices y adecuación, I (3rd edition).Juan Pablo Jorge & Federico Holik - 2022 - Teorema: International Journal of Philosophy 41 (3):65-88.
    In this paper we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics. We give a characterization of the degree of non-functionality which is compatible with the propositional structure of quantum theory, showing that having truth-functional connectives, together with some assumptions regarding the relation of logical consequence, commits us to the adequacy of the interpretation sets of these connectives. An advantage of our proof is that it is independent of (...)
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  10.  40
    Retornando al Hotel de Hilbert.Juan Pablo Jorge & Hernán Luis Vázquez - 2021 - Revista de Educación Matemática 36 (2):67-87.
    Some partitions of Natural Number set are built through recursive processesgenerating in this manner countable examples of countable and disjoint sets whose unionis a set also countable. This process is constructive, so the Axiom of choice is not used.We provide a PC program that generates one of these special partitions and shows howto generate infinite of them. This line of reasoning can have multiple applications in Settheory and Model theory. We proved that the number of ways to make these partitionsof (...)
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