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33Brouwer-Zadeh logic and the operational approach to quantum mechanicsFoundations of Physics 20 (6): 701-714. 1990.This paper is concerned with a logical system, called Brouwer-Zadeh logic, arising from the BZ poset of all effects of a Hilbert space. In particular, we prove a representation theorem for Brouwer-Zadeh lattices, and we show that Brouwer-Zadeh logic is not characterized by the MacNeille completions of all BZ posets of effects
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24On the Notion of “Law”Vienna Circle Institute Yearbook 9 1-11. 2002.The term “law” appears in different contexts with different meanings. We are used to speaking of natural laws, legal laws, moral laws, aesthetic laws, historical laws. Such a linguistic convention has represented a constant phenomenon through the history of civilization. Is there any deep common root among all these different uses and meanings?
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24Constructivism and Operationalism in the Foundations of Quantum MechanicsVienna Circle Institute Yearbook 3 21-31. 1995.The debate about constructivism in physics has led to different kinds of questions that can be conventionally framed in two classes. One concerns the mathematics that is considered for the theoretical development of physics. The other is concerned with the experimental parts of physical theories. It is unnecessary to observe that the intersection between our two classes of problems is far from being empty. In this paper we will mainly deal with topics belonging to the second class. However, let …Read more
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Quantum Logic and Hidden VariablesJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 26 (2): 345-348. 1995.
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19On the Structure of Pseudo BL-algebras and Pseudo Hoops in Quantum LogicsFoundations of Physics 40 (9-10): 1519-1542. 2010.The main aim of the paper is to solve a problem posed in Di Nola et al. (Multiple Val. Logic 8:715–750, 2002) whether every pseudo BL-algebra with two negations is good, i.e. whether the two negations commute. This property is intimately connected with possessing a state, which in turn is essential in quantum logical applications. We approach the solution by describing the structure of pseudo BL-algebras and pseudo hoops as important families of quantum structures. We show when a pseudo hoop can…Read more
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178Entanglement as a Semantic ResourceFoundations of Physics 40 (9-10): 1494-1518. 2010.The characteristic holistic features of the quantum theoretic formalism and the intriguing notion of entanglement can be applied to a field that is far from microphysics: logical semantics. Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities: systems of qubits (quregisters) or, more generally, mixtures of quregi…Read more
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10The unsharp approaches to quantum mechanicsIn HerfelWilliam (ed.), Theories and Models in Scientific Processes, Rodopi. pp. 345. 1995.
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50Brouwer-Zadeh logic, decidability and bimodal systemsStudia Logica 51 (1). 1992.We prove that Brouwer-Zadeh logic has the finite model property and therefore is decidable. Moreover, we present a bimodal system (BKB) which turns out to be characterized by the class of all Brouwer-Zadeh frames. Finally, we show that BrouwerZadeh logic can be translated into BKB.
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41Paraconsistent quantum logicsFoundations of Physics 19 (7): 891-904. 1989.Paraconsistent quantum logics are weak forms of quantum logic, where the noncontradiction and the excluded-middle laws are violated. These logics find interesting applications in the operational approach to quantum mechanics. In this paper, we present an axiomatization, a Kripke-style, and an algebraic semantical characterization for two forms of paraconsistent quantum logic. Further developments are contained in Giuntini and Greuling's paper in this issue
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38Partial and unsharp quantum logicsFoundations of Physics 24 (8): 1161-1177. 1994.The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples of these structures. Fi…Read more
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72Fuzzy intuitionistic quantum logicsStudia Logica 52 (3). 1993.Fuzzy intuitionistic quantum logics (called also Brouwer-Zadeh logics) represent to non standard version of quantum logic where the connective not is split into two different negation: a fuzzy-like negation that gives rise to a paraconsistent behavior and an intuitionistic-like negation. A completeness theorem for a particular form of Brouwer-Zadeh logic (BZL 3) is proved. A phisical interpretation of these logics can be constructed in the framework of the unsharp approach to quantum theory.
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59Quantum MV algebrasStudia Logica 56 (3). 1996.We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.
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Alle origini del problema delle variabili nascoste in meccanica quantisticaRivista di Filosofia 78 (1): 89-109. 1987.