30 found
Order:
See also
  1.  69
    MV-Algebras and Quantum Computation.Antonio Ledda, Martinvaldo Konig, Francesco Paoli & Roberto Giuntini - 2006 - Studia Logica 82 (2):245-270.
    We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   8 citations  
  2.  57
    Expanding Quasi-MV Algebras by a Quantum Operator.Roberto Giuntini, Antonio Ledda & Francesco Paoli - 2007 - Studia Logica 87 (1):99-128.
    We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  3. Entanglement as a Semantic Resource.Maria Luisa Dalla Chiara, Roberto Giuntini, Antonio Ledda, Roberto Leporini & Giuseppe Sergioli - 2010 - Foundations of Physics 40 (9-10):1494-1518.
    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 quregisters (qumixes), while logical connectives are interpreted as special (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  4.  9
    Toward a Formal Language for Unsharp Properties.Roberto Giuntini & Heinz Greuling - 1989 - Foundations of Physics 19 (7):931-945.
    Some algebraic structures of the set of all effects are investigated and summarized in the notion of a(weak) orthoalgebra. It is shown that these structures can be embedded in a natural way in lattices, via the so-calledMacNeille completion. These structures serve as a model ofparaconsistent quantum logic, orthologic, andorthomodular quantum logic.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   12 citations  
  5.  13
    Paraconsistent Quantum Logics.Maria Luisa Dalla Chiara & Roberto Giuntini - 1989 - Foundations of Physics 19 (7):891-904.
    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.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   9 citations  
  6. On Some Properties of Quasi-MV Algebras and $\Sqrt{^{\Prime }}$ Quasi-MV Algebras.Francesco Paoli, Antonio Ledda, Roberto Giuntini & Hector Freytes - 2009 - Reports on Mathematical Logic:31-63.
    We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in terms of algebras of functions; (...)
     
    Export citation  
     
    My bibliography   3 citations  
  7.  24
    The Algebraic Structure of an Approximately Universal System of Quantum Computational Gates.Maria Luisa Dalla Chiara, Roberto Giuntini, Hector Freytes, Antonio Ledda & Giuseppe Sergioli - 2009 - Foundations of Physics 39 (6):559-572.
  8. Paraconsistent Ideas in Quantum Logic.Maria Luisa Dalla Chiara & Roberto Giuntini - 2000 - Synthese 125 (1/2):55-68.
  9.  37
    The Logics of Orthoalgebras.Maria Luisa Dalla Chiara & Roberto Giuntini - 1995 - Studia Logica 55 (1):3-22.
    The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp orthoalgebras is isomorphic to the category of D-posets. A completeness theorem for some partial logics based on unsharp orthoalgebras, orthoalgebras and orthomodular posets is proved.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  10.  3
    Brouwer-Zadeh Logic and the Operational Approach to Quantum Mechanics.Roberto Giuntini - 1990 - Foundations of Physics 20 (6):701-714.
    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.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  11.  13
    A Semantical Investigation on Brouwer-Zadeh Logic.Roberto Giuntini - 1991 - Journal of Philosophical Logic 20 (4):411 - 433.
    In the standard approach to quantum mechanics, closed subspaces of a Hilbert space represent propositions. In the operational approach, closed subspaces are replaced by effects that represent a mathematical counterpart for properties which can be measured in a physical system. Effects are a proper generalization of closed subspaces. Effects determine a Brouwer-Zadeh poset which is not a lattice. However, such a poset can be embedded in a complete Brouwer-Zadeh lattice. From an intuitive point of view, one can say that these (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  12.  35
    Quantum MV Algebras.Roberto Giuntini - 1996 - Studia Logica 56 (3):393 - 417.
    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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  13.  22
    Some Results on BZ Structures From Hilbertian Unsharp Quantum Physics.Gianpiero Cattaneo & Roberto Giuntini - 1995 - Foundations of Physics 25 (8):1147-1183.
    Some algebraic structures determined by the class σ(þ) of all effects of a Hilbert space þ and by some subclasses of σ(þ) are investigated, in particular de Morgan-Brouwer-Zadeh posets [it is proved that σ(þ n )(n<∞) has such a structure], Brouwer-Zadeh * posets (a quite trivial example consisting of suitable effects is given), and Brouwer-Zadeh 3 posets which are both de Morgan and *.It is shown that a nontrivial class of effects of a Hilbert space exists which is a BZ (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  14.  3
    Partial and Unsharp Quantum Logics.Maria Luisa Dalla Chiara & Roberto Giuntini - 1994 - Foundations of Physics 24 (8):1161-1177.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  15. Quantum Logic and Hidden Variables.Roberto Giuntini & Reiner Hedrich - 1995 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 26 (2):345-348.
  16.  30
    The Toffoli-Hadamard Gate System: An Algebraic Approach.Maria Luisa Dalla Chiara, Antonio Ledda, Giuseppe Sergioli & Roberto Giuntini - 2013 - Journal of Philosophical Logic 42 (3):467-481.
    Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbert-space quantum computational structures, by introducing the notion of Toffoli-Hadamard algebra. From an intuitive point of (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  17.  10
    A New View of Effects in a Hilbert Space.Roberto Giuntini, Antonio Ledda & Francesco Paoli - 2016 - Studia Logica 104 (6):1145-1177.
    We investigate certain Brouwer-Zadeh lattices that serve as abstract counterparts of lattices of effects in Hilbert spaces under the spectral ordering. These algebras, called PBZ*-lattices, can also be seen as generalisations of orthomodular lattices and are remarkable for the collapse of three notions of “sharpness” that are distinct in general Brouwer-Zadeh lattices. We investigate the structure theory of PBZ*-lattices and their reducts; in particular, we prove some embedding results for PBZ*-lattices and provide an initial description of the lattice of PBZ*-varieties.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  18.  1
    Fuzzy-Intuitionistic Quantum Logic.Maria Luisa Dalla Chiara, Gianpiero Cattaneo & Roberto Giuntini - 1993 - Studia Logica 52 (1):24.
  19.  11
    On the Notion of “Law”.Maria Dalla Chiara & Roberto Giuntini - 2002 - Vienna Circle Institute Yearbook 9:1-11.
    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?
    Direct download  
     
    Export citation  
     
    My bibliography  
  20.  31
    Fuzzy Intuitionistic Quantum Logics.Gianpiero Cattaneo, Maria L. Dalla Chiara & Roberto Giuntini - 1993 - Studia Logica 52 (3):419 - 442.
    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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  21.  11
    Holism and Contextuality: A Quantum-Like Semantics for Music.Maria Chiara, Roberto Giuntini & Eleonora Negri - 2010 - Manuscrito 33 (1).
    Direct download  
     
    Export citation  
     
    My bibliography  
  22.  9
    Łukasiewicz’ Theory of Truth, From the Quantum Logical Point of View.Maria Dalla Chiara & Roberto Giuntini - 1999 - Vienna Circle Institute Yearbook 6:127-134.
    In 1920 Łukasiewicz published a two-page article whose title was “On Three-valued Logic”. The paper proposes a semantic characterization for the logic that has been later called Ł3 . In spite of the shortness of the paper, all the important points concerning the semantics of Ł3 are already there and can be naturally generalized to the case of a generic number n of truth-values . The conclusion of the article is quite interesting:The present author is of the opinion that three-valued (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  23.  9
    The Impossible Causality: The No Hidden Variables Theorem of John von Neumann.Roberto Giuntini & Federico Laudisa - 2001 - Vienna Circle Institute Yearbook 8:173-188.
    The debate over the question whether quantum mechanics should be considered as a complete account of microphenomena has a long and deeply involved history, a turning point in which has been certainly the Einstein-Bohr debate, with the ensuing charge of incompleteness raised by the Einstein-Podolsky-Rosen argument. In quantum mechanics, physical systems can be prepared in pure states that nevertheless have in general positive dispersion for most physical quantities; hence in the EPR argument, the attention is focused on the question whether (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  24.  24
    Brouwer-Zadeh Logic, Decidability and Bimodal Systems.Roberto Giuntini - 1992 - Studia Logica 51 (1):97 - 112.
    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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  25.  16
    Quantum Logics and Lindenbaum Property.Roberto Giuntini - 1987 - Studia Logica 46 (1):17 - 35.
    This paper will take into account the Lindenbaum property in Orthomodular Quantum Logic (OQL) and Partial Classical Logic (PCL). The Lindenbaum property has an interest both from a logical and a physical point of view since it has to do with the problem of the completeness of quantum theory and with the possibility of extending any semantically non-contradictory set of formulas to a semantically non-contradictory complete set of formulas. The main purpose of this paper is to show that both OQL (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  26.  6
    Hector Freytes, Antonio Ledda, Giuseppe Sergioli And.Roberto Giuntini & Probabilistic Logics in Quantum Computation - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao González, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer Verlag. pp. 49.
    Direct download  
    Translate
     
     
    Export citation  
     
    My bibliography  
  27.  2
    The Unsharp Approaches to Quantum Mechanics.Gianpiero Cattaneo, Maria Luisa Dalla Chiara & Roberto Giuntini - 1995 - In HerfelWilliam (ed.), Theories and Models in Scientific Processes. Rodopi. pp. 345.
    Direct download  
     
    Export citation  
     
    My bibliography  
  28. History of Philosophy of Science: New Trends and Perspectives.Maria Luisa Dalla Chiara, Roberto Giuntini, Marina Frasca-Spada, Lothar Schäfer, Kenneth Simonsen & R. Lanier Anderson - 2002 - Springer Verlag.
  29. Language, Quantum, Music Selected Contributed Papers of the Tenth International Congress of Logic, Methodology, and Philosophy of Science, Florence, August 1995.Maria Luisa Dalla Chiara, Roberto Giuntini & Federico Laudisa - 1999
     
    Export citation  
     
    My bibliography  
  30. Quantum Information, Cognition, and Music.Maria L. Dalla Chiara, Roberto Giuntini, Roberto Leporini, Eleonora Negri & Giuseppe Sergioli - 2015 - Frontiers in Psychology 6.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography