93 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
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
An Holistic Extension for Classical Logic via Quantum Fredkin Gate
An holistic extension for classical propositional logic is introduced in the framework of
quantum computation with mixed states. The mentioned extension is obtained by applying the
quantum Fredkin gate to non-factorizable bipartite states. In particular, an extended notion of
classical contradiction is studied in this holistic framework
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