Systems of Quantum Logic

被引：0

作者：

Satoko Titani

Heiji Kodera

Hiroshi Aoyama

机构：

[1] Chubu University,Faculty of Humanities

[2] Aichi University of Education,undefined

[3] Tokaigakuen University,undefined

来源：

Studia Logica | 2013年 / 101卷

关键词：

Logic; Modality; Quantum theory; Set theory;

D O I：

暂无

中图分类号：

学科分类号：

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：24