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Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Humanities and Human Sciences / Faculty of Humanities and Human Sciences >
哲学 = Annals of the Philosophical Society of Hokkaido University >
第52号 中戸川孝治教授退職記念号 >
非可換部分構造論理における量子論理の含意について
| Title: | 非可換部分構造論理における量子論理の含意について |
| Other Titles: | On Implicational Connectives of Quantum Logics analyzed in Gentzen-style Natural Deduction for Non-commutative Substructural Logics |
| Authors: | 上野, 岳史1 Browse this author |
| Authors(alt): | UENO, Takesh1 |
| Issue Date: | 2-Dec-2018 |
| Publisher: | 北海道大学哲学会 |
| Journal Title: | 哲学 |
| Journal Title(alt): | Annals of the Philosophical Society of Hokkaido University |
| Volume: | 52 |
| Start Page: | 71 |
| End Page: | 90 |
| Abstract: | Birkhoff and von Neumann introduced Quantum Logic, in which the commonly agreed definition of the implicational connective has not yet achieved. Kotas proposed six formulations to define six implicational connectives. Ozawa introduced symmetrical relations among these implicational connectives. NFL is a Gentzen-style natural deduction for non-commutative substructural logic, which excludes three structural inference rules, i.e. contraction, weakening and exchange. We wll construct proof figures of NFL, augmented with other inference rules, to establish relations among the implicational connectives, so that the relevancies of inference rules, including structural rules such as exchange rule, are clarified. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/75452 |
| Appears in Collections: | 哲学 = Annals of the Philosophical Society of Hokkaido University > 第52号 中戸川孝治教授退職記念号
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