786 research outputs found
Pavelka-style completeness in expansions of \L ukasiewicz logic
An algebraic setting for the validity of Pavelka style completeness for some
natural expansions of \L ukasiewicz logic by new connectives and rational
constants is given. This algebraic approach is based on the fact that the
standard MV-algebra on the real segment is an injective MV-algebra. In
particular the logics associated with MV-algebras with product and with
divisible MV-algebras are considered
Fuzzy approach for CNOT gate in quantum computation with mixed states
In the framework of quantum computation with mixed states, a fuzzy
representation of CNOT gate is introduced. In this representation, the
incidence of non-factorizability is specially investigated.Comment: 14 pages, 2 figure
The Contextual Character of Modal Interpretations of Quantum Mechanics
In this article we discuss the contextual character of quantum mechanics in
the framework of modal interpretations. We investigate its historical origin
and relate contemporary modal interpretations to those proposed by M. Born and
W. Heisenberg. We present then a general characterization of what we consider
to be a modal interpretation. Following previous papers in which we have
introduced modalities in the Kochen-Specker theorem, we investigate the
consequences of these theorems in relation to the modal interpretations of
quantum mechanics.Comment: 21 pages, no figures, preprint submitted to SHPM
Two-valued states on Baer -semigroups
In this paper we develop an algebraic framework that allows us to extend
families of two-valued states on orthomodular lattices to Baer -semigroups.
We apply this general approach to study the full class of two-valued states and
the subclass of Jauch-Piron two-valued states on Baer -semigroups.Comment: Reports on mathematical physics (accepted 2013
Quantum field logic
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of
the structure of relativistic quantum mechanics. It is formulated in terms of a
net of operator algebras indexed by regions of a Lorentzian manifold. In
several cases the mentioned net is represented by a family of von Neumann
algebras, concretely, type III factors. Local quantum field logic arises as a
logical system that captures the propositional structure encoded in the
algebras of the net. In this framework, this work contributes to the solution
of a family of open problems, emerged since the 30s, about the characterization
of those logical systems which can be identified with the lattice of projectors
arising from the Murray-von Neumann classification of factors. More precisely,
based on physical requirements formally described in AQFT, an equational theory
able to characterizethe type III condition in a factor is provided. This
equational system motivates the study of a variety of algebras having an
underlying orthomodular lattice structure. A Hilbert style calculus,
algebraizable in the mentioned variety, is also introduced and a corresponding
completeness theorem is established
Pattern Recognition In Non-Kolmogorovian Structures
We present a generalization of the problem of pattern recognition to
arbitrary probabilistic models. This version deals with the problem of
recognizing an individual pattern among a family of different species or
classes of objects which obey probabilistic laws which do not comply with
Kolmogorov's axioms. We show that such a scenario accommodates many important
examples, and in particular, we provide a rigorous definition of the classical
and the quantum pattern recognition problems, respectively. Our framework
allows for the introduction of non-trivial correlations (as entanglement or
discord) between the different species involved, opening the door to a new way
of harnessing these physical resources for solving pattern recognition
problems. Finally, we present some examples and discuss the computational
complexity of the quantum pattern recognition problem, showing that the most
important quantum computation algorithms can be described as non-Kolmogorovian
pattern recognition problems
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