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Holistic Type Extension for Classical Logic via Toffoli Quantum Gate.

Hector Freytes1, Roberto Giuntini1,2, Giuseppe Sergioli1

  • 1Dipartimento di Filosofia, University of Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy.

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Summary
This summary is machine-generated.

This study introduces a holistic logic extension using quantum computation, revealing how quantum states alter classical logic concepts like contradiction. This quantum logic framework incorporates irreversible transformations.

Keywords:
fuzzy logicquantum Toffoli gatequantum computational logic

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Area of Science:

  • Quantum Information Science
  • Quantum Computation
  • Quantum Logic

Background:

  • Classical propositional logic provides a foundation for reasoning.
  • Quantum computation offers novel frameworks for information processing.
  • Mixed quantum states and irreversible transformations are key aspects of quantum information theory.

Purpose of the Study:

  • To introduce a holistic extension of classical propositional logic.
  • To explore the formal aspects of this new quantum logical system.
  • To investigate the concepts of tautology and contradiction within this extended framework.

Main Methods:

  • Utilizing the Toffoli quantum gate as a basis for logical operations.
  • Employing the framework of quantum computation with mixed states.
  • Analyzing the impact of non-separable quantum states on logical concepts.

Main Results:

  • A novel holistic extension of propositional logic is established.
  • The concepts of tautology and contradiction are shown to undergo significant changes.
  • Werner states are identified as specific instances of holistic contradiction.

Conclusions:

  • Quantum mechanics fundamentally alters classical logical structures.
  • The non-separability of quantum states introduces new forms of logical relationships.
  • This work bridges quantum computation and formal logic systems.