12 found
Order:
  1.  21
    Axiomatic Unsharp Quantum Theory (From Mackey to Ludwig and Piron).Gianpiero Cattaneo & Federico Laudisa - 1994 - Foundations of Physics 24 (5):631-683.
    On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a “state-event-probability” (SEVP) structure, using a quite standard “fuzzification” procedure, a set of unsharp events (or “effects”) is constructed and the corresponding “state-effect-probability” (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  2.  17
    Fuzzy-Intuitionistic Quantum Logic.Maria Luisa Dalla Chiara, Gianpiero Cattaneo & Roberto Giuntini - 1993 - Studia Logica 52 (1):24.
  3.  53
    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 (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  4.  34
    Generalized Rough Sets (Preclusivity Fuzzy-Intuitionistic (BZ) Lattices).Gianpiero Cattaneo - 1997 - Studia Logica 58 (1):47-77.
    The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (indiscernibility) relation R U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the "elementary" (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  5.  29
    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  
     
    Bookmark   2 citations  
  6.  26
    Algebraic Structures Arising in Axiomatic Unsharp Quantum Physics.Gianpiero Cattaneo & Stanley Gudder - 1999 - Foundations of Physics 29 (10):1607-1637.
    This article presents and compares various algebraic structures that arise in axiomatic unsharp quantum physics. We begin by stating some basic principles that such an algebraic structure should encompass. Following G. Mackey and G. Ludwig, we first consider a minimal state-effect-probability (minimal SEFP) structure. In order to include partial operations of sum and difference, an additional axiom is postulated and a SEFP structure is obtained. It is then shown that a SEFP structure is equivalent to an effect algebra with an (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  16
    A Note on Aerts' Description of Separated Entities.Gianpiero Cattaneo & Giuseppe Nisticò - 1990 - Foundations of Physics 20 (1):119-132.
    The theoretical scheme proposed by Aerts for describing two separated entities as a whole within a question-state structure is considered. The quoted author claims that two relevant axioms characterizing quantum physics cannot hold for a quantum, nonclassical entity consisting of two quantum separate entities. We suggest that Aerts' theory is not adequate, from the empirical point of view, to describe this situation.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  46
    A Concrete Procedure for Obtaining Sharp Reconstructions of Unsharp Observables in Finite-Dimensional Quantum Mechanics.Gianpiero Cattaneo, Tiziana Marsico, Giuseppe Nisticò & Guido Bacciagaluppi - 1997 - Foundations of Physics 27 (10):1323-1343.
    We discuss the problem of how a (commutative) generalized observable in a finite-dimensional Hilbert space (communtative effect-valued resolution of the identity) can be considered as an unsharp realization of some standard observable (projection-valued resolution of the identity). In particular, we give a concrete procedure for constructing such a standard observable. Some results about the “uniqueness” of the resulting observable are also examined.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  9.  17
    Coexistence of Questions Versus Piron's Compatibility.Gianpiero Cattaneo & Giuseppe Nisticò - 1994 - Foundations of Physics 24 (8):1131-1152.
    The notion of coexistence between questions is introduced in the framework of Piron's approach to quantum physics, using Aerts' notion of performable-together questions. Relationships between coexistence of questions and Piron's compatibility of propositions are investigated. In particular, properties generated by coexistent and primitive questions are compatible.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  10. Fuzziness in Italy – Traces of a Scattered History.Gianpiero Cattaneo, Giulianella Coletti, Antonio Di Nola, Mario Fedrizzi, Giangiacomo Gerla, Gabriella Pasi, Marco Elio Tabacchi, Settimo Termini & Aldo Ventre - 2017 - Archives for the Philosophy and History of Soft Computing 2017 (1).
    The history of Fuzziness in Italy is varied and scattered among a num- ber of research groups. As a matter of fact, “fuzziness” spread in Italy through a sort of spontaneous diffusion, and, also subsequently, no one felt the need to cre- ate some “national” common structure like an Association or similar things. Since a cohesive retelling would be next to impossible, a few members of the Italian fuzzy community have been asked to recount their experience and express their hopes (...)
    No categories
     
    Export citation  
     
    Bookmark  
  11.  14
    Individual Samples, Preparations, and States in Piron's Approach to Quantum Physics.Gianpiero Cattaneo, Tiziana Marsico & Giuseppe NisticÒ - 1994 - Foundations of Physics 24 (9):1293-1303.
    The mathematical description of the three distinct fundamental notions of “individual sample” of “preparing procedure,” and of “Piron's state” of a physical entity are precisely introduced in the framework of the Piron's “preparation-question structure” (without specific axioms C, P, A) based on Ludwig's “selection structure.” We compare our realization of the above notions with a similar use of the standard terminology of the “Geneva School” adopted by Pykacz and Santos in a recent paper.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  12.  4
    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  
     
    Bookmark