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Intuitionistic Quantum Logic Perspective: A New Approach to Natural Revision Theory

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arXiv:2404.13608v1 Announce Type: new
Abstract: The classical belief revision framework proposed by Alchourron, Gardenfors, and Makinson involves the revision of a theory based on eight postulates. This paper focuses on exploring the revision theory based on quantum mechanics, known as the natural revision theory. In quantum systems, there are two reasoning modes: static intuitionistic reasoning, which incorporates contextuality, and dynamic reasoning, which is achieved through projection measurement.
We combine the advantages of the two intuitionistic quantum logics proposed by Doering and Coecke respectively. We aim to provide a truth-value assignment for intuitionistic quantum logic that not only aligns with the characteristics of quantum mechanics but also allows for truth-value reasoning. We investigate the natural revision theory based on this approach.
We introduce two types of revision operators corresponding to the two reasoning modes in quantum systems: object-level revision and operator-level revision, and we highlight the distinctions between these two operators. Unlike classical revision, we consider the revision of consequence relations in intuitionistic quantum logic. We demonstrate that, within the framework of the natural revision theory, both types of revision operators work together on the reasoning system of consequence relations. The outcomes of revision process are influenced by the order in which the interweaved operators are applied.

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