The Logic of Quasi-MV Algebras

被引:20
作者
Bou, Felix [1 ]
Paoli, Francesco [2 ]
Ledda, Antonio [2 ]
Spinks, Matthew [3 ]
Giuntini, Roberto [2 ]
机构
[1] IIIA CSIC, Artificial Intelligence Res Inst, Bellaterra, Spain
[2] Univ Cagliari, Dept Educ, Cagliari, Italy
[3] Univ Bern, Math Inst, Bern, Switzerland
关键词
Quasi-MV algebras; quantum computation; MV algebras; abstract algebraic logic; VARIETIES; TRUTH;
D O I
10.1093/logcom/exp080
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
The algebraic theory of quasi-MV algebras, generalizations of MV algebras arising in quantum computation, is by now rather well-developed. Although it is possible to define several interesting logics from these structures, so far this aspect has not been investigated. The present article aims at filling this gap.
引用
收藏
页码:619 / 643
页数:25
相关论文
共 26 条
[1]  
Andreka H., 2001, Handbook of Philosophical Logic, V2, P133
[2]  
[Anonymous], 1990, B POLISH ACAD SCI SE
[3]  
[Anonymous], 2001, PROTOALGEBRAIC LOGIC
[4]  
[Anonymous], 1989, Memoirs of the American Mathematical Society
[5]   Algebras defined from ordered sets and the varieties they generate [J].
Berman, J. ;
Blok, W. J. .
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2006, 23 (01) :65-88
[6]   Assertionally equivalent quasivarieties [J].
Blok, W. J. ;
Raftery, J. G. .
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2008, 18 (04) :589-681
[7]  
Bou F, 2008, SOFT COMPUT, V12, P341, DOI 10.1007/s00500-007-0185-8
[8]   Logics Preserving Degrees of Truth from Varieties of Residuated Lattices [J].
Bou, Felix ;
Esteva, Francesc ;
Font, Josep Maria ;
Gil, Angel J. ;
Godo, Lluis ;
Torrens, Antoni ;
Verdu, Ventura .
JOURNAL OF LOGIC AND COMPUTATION, 2009, 19 (06) :1031-1069
[9]  
Chang C.C., 1958, T AM MATH SOC, V88, P467
[10]  
Cignoli R., 2000, TRENDS LOGIC, V7