Systems of Quantum Logic

被引：0

作者：

Titani, Satoko ^{[1
]}

Kodera, Heiji ^{[2
]}

Aoyama, Hiroshi ^{[3
]}

机构：

[1] Chubu Univ, Kasugai, Aichi 4878501, Japan

[2] Aichi Univ Educ, Kariya, Aichi 4488542, Japan

[3] Tokaigakuen Univ, Fac Humanities, Nagoya, Aichi 4688514, Japan

来源：

STUDIA LOGICA | 2013年 / 101卷 / 01期

关键词：

Logic; Modality; Quantum theory; Set theory;

D O I：

10.1007/s11225-011-9364-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Logical implications are closely related to modal operators. Lattice-valued logic LL and quantum logic QL were formulated in Titani S (1999) Lattice Valued Set Theory. Arch Math Logic 38:395-421, Titani S (2009) A Completeness Theorem of Quantum Set Theory. In: Engesser K, Gabbay DM, Lehmann D (eds) Handbook of Quantum Logic and Quantum Structures: Quantum Logic. Elsevier Science Ltd., pp. 661-702, by introducing the basic implication -> which represents the lattice order. In this paper, we fomulate a predicate orthologic provided with the basic implication, which corresponds to complete ortholattices, and then formulate a quantum logic which is equivalent to QL, by using a modal operator instead of the basic implication.

引用

页码：193 / 217

页数：25

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