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arXiv · 2610.40807

On the Reconstruction of Orthomodular Logic via Restricted Negation

Tomoaki Kawano·Ryo Kashima
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Abstract

Orthomodular logic has long been studied as a fundamental logical framework within quantum logic. In addition to its lattice-theoretic foundations, various formulations have been proposed that incorporate specialized implication connectives and more complex logical connectives. In this study, we reconstruct orthomodular logic by introducing a connective referred to as restricted negation, which has received comparatively little attention in the existing literature. We demonstrate that this connective provides a natural and expressive basis for formulating the core principles of orthomodular logic. Furthermore, as a main result, we construct a new proof system for orthomodular logic founded on this connective.

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Tomoaki Kawano, Ryo Kashima. 2026-10-29. On the Reconstruction of Orthomodular Logic via Restricted Negation. https://doi.org/10.4204/eptcs.455.5

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