Pattern Recognition in Non-Kolmogorovian Structures

Foundations of Science 23 (1):119-132 (2018)
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Abstract

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 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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Citations of this work

Towards a Multi Target Quantum Computational Logic.Giuseppe Sergioli - 2020 - Foundations of Science 25 (1):87-104.

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References found in this work

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Quantum probability theory.Miklós Rédei & Stephen Jeffrey Summers - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):390-417.

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