On Implicational Connectives of Quantum Logics analyzed in Gentzen-style Natural Deduction for Non-commutative Substructural Logics
Bibliographic Information
- Other Title
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- 非可換部分構造論理における量子論理の含意について
- ヒカカンブブン コウゾウ ロンリ ニ オケル リョウシ ロンリ ノ ガン イ ニ ツイテ
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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.
Journal
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- Annals of the Philosophical Society of Hokkaido University
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Annals of the Philosophical Society of Hokkaido University 52 71-90, 2018-12-02
北海道大学哲学会
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Details 詳細情報について
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- CRID
- 1050001339063779584
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- NII Article ID
- 120006723669
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- NII Book ID
- AN0015042X
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- HANDLE
- 2115/75452
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- NDL BIB ID
- 029493521
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- ISSN
- 02872560
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- Text Lang
- ja
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- Article Type
- departmental bulletin paper
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- Data Source
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- IRDB
- NDL
- CiNii Articles