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Quantum cognition based on an ambiguous representation derived from a rough set approximation.

Yukio-Pegio Gunji1, Kohei Sonoda2, Vasileios Basios3

  • 1Department of Intermedia Art and Science, School of Fundamental Science and Technology, Waseda University, Ohkubo 3-4-1, Shinjuku, Tokyo 169-8555, Japan.

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Summary

Decision-making processes, modeled as inverse Bayes inference on neuron spike trains, exhibit quantum-like characteristics. This study reveals their logical structure aligns with quantum logic, not Boolean logic, due to ambiguous representations.

Keywords:
Bayes inferenceCognitionInverse Bayes inferenceOrtho-modular latticeQuantum logic

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Area of Science:

  • Cognitive Science
  • Quantum Physics
  • Information Theory

Background:

  • A previously proposed model describes decision-making as inverse Bayes inference on neuron spike trains.
  • This inference, when applied to successive stimuli, shows quantum-like characteristics.

Purpose of the Study:

  • To investigate the relationship between decision-making processes and ambiguous representations.
  • To reveal the underlying logical structure of inverse Bayes inference in cognitive processes.

Main Methods:

  • Defined ambiguous representation using a pair of interrelated maps.
  • Replaced prior/posterior hypotheses with upper/lower approximations from rough set analysis.
  • Implemented inverse Bayes inference using combined approximations from the maps.

Main Results:

  • The decision-making process is consistently related to ambiguous representations.
  • The logical structure of combined approximations forms an orthomodular lattice.
  • This structure necessitates representation by quantum logic, not Boolean logic.

Conclusions:

  • This work demonstrates a concrete link between inverse Bayes inference in decision-making and quantum logic.
  • The findings suggest that cognitive processes may inherently follow quantum principles.
  • This is the first study to elucidate the specific quantum logical structure of inverse Bayes inference in cognition.