Computer Science ›› 2016, Vol. 43 ›› Issue (Z6): 21-24.doi: 10.11896/j.issn.1002-137X.2016.6A.003

Previous Articles     Next Articles

Distributive Law in Deduction Mechanism of Logic

SHI Hang, WANG Bao-shan and WU Mei-hua   

  • Online:2018-12-01 Published:2018-12-01

Abstract: It is well known that the distributive law plays a core role in deduction mechanism of classical logic.How-ever,distributive law is abandoned in quantum logic,so that the classic deduction mechanism disappears from quantum,which spontaneously arises the debate whether the quantum logic can be called “logic”? In this paper,we introduced the defects of using closed subspaces of Hilbert space to describe quantum logic and deeply analyzed the deduction mechanism in classical logic.Further,the deduction mechanism can be established in quantum logic by using the orthomodular law instead of distributive law.In particular,the deduction mechanism can be renewed with adjunctions in category,which is a generalization of deduction mechanism in classical logic.

Key words: Distributive law,Deduction mechanism,Orthomodular law,Adjunctions

[1] Brikhoff G,von Neumann J.The logic of quantum mechanics[M].Annals of Mathematics,1936,37(4):823-843
[2] de Vries A.Algebra Hierarchy of logics unifying fuzzy logic and quantum logic.
[3] Mackey G W.Mathematical foundations of quantum mechanics[M].Benjamin,New York,1936
[4] Coecke B,Smets S.The Sasaki Hook is not a Implicative Connective but Induces a Backward[in Time] Dynamic One that Assigns Causes.
[5] Aerts D,D’Hondt E,Gabora L.Why the Disjunction in Quantum Logic is Not Classical?[J].Foundations of Physics,2000,0(9):1473
[6] Birkhoff G.Lattice Theory[M].American Mathematical Society,Providence,1940
[7] Russo C.Quantale Modules and their Operators,with Applications[J].Joural of Logic Computation,2010,0(4):917-946
[8] Abramsky S,Tzevelekos N.Introduction to Categories and Categorical Logic[M].Springer-Verlag Berlin Heidelberg ,2011
[9] 任芳.互为伴随的三角模与蕴涵算子及蕴涵算子的逼近问题[D].西安:陕西师范大学,2001

No related articles found!
Full text



[1] LEI Li-hui and WANG Jing. Parallelization of LTL Model Checking Based on Possibility Measure[J]. Computer Science, 2018, 45(4): 71 -75, 88 .
[2] XIA Qing-xun and ZHUANG Yi. Remote Attestation Mechanism Based on Locality Principle[J]. Computer Science, 2018, 45(4): 148 -151, 162 .
[3] LI Bai-shen, LI Ling-zhi, SUN Yong and ZHU Yan-qin. Intranet Defense Algorithm Based on Pseudo Boosting Decision Tree[J]. Computer Science, 2018, 45(4): 157 -162 .
[4] WANG Huan, ZHANG Yun-feng and ZHANG Yan. Rapid Decision Method for Repairing Sequence Based on CFDs[J]. Computer Science, 2018, 45(3): 311 -316 .
[5] SUN Qi, JIN Yan, HE Kun and XU Ling-xuan. Hybrid Evolutionary Algorithm for Solving Mixed Capacitated General Routing Problem[J]. Computer Science, 2018, 45(4): 76 -82 .
[6] ZHANG Jia-nan and XIAO Ming-yu. Approximation Algorithm for Weighted Mixed Domination Problem[J]. Computer Science, 2018, 45(4): 83 -88 .
[7] WU Jian-hui, HUANG Zhong-xiang, LI Wu, WU Jian-hui, PENG Xin and ZHANG Sheng. Robustness Optimization of Sequence Decision in Urban Road Construction[J]. Computer Science, 2018, 45(4): 89 -93 .
[8] LIU Qin. Study on Data Quality Based on Constraint in Computer Forensics[J]. Computer Science, 2018, 45(4): 169 -172 .
[9] ZHONG Fei and YANG Bin. License Plate Detection Based on Principal Component Analysis Network[J]. Computer Science, 2018, 45(3): 268 -273 .
[10] SHI Wen-jun, WU Ji-gang and LUO Yu-chun. Fast and Efficient Scheduling Algorithms for Mobile Cloud Offloading[J]. Computer Science, 2018, 45(4): 94 -99, 116 .