Bounded commutative residuated l-monoids with general comparability and states

被引：20
作者：
Dvurecenskij, A
Rachunek, J
机构：
[1] Slovak Acad Sci, Inst Math, SK-81473 Bratislava, Slovakia
[2] Palacky Univ, Fac Sci, Dept Algebra & Geometry, CZ-77900 Olomouc, Czech Republic
来源：
SOFT COMPUTING | 2006年 / 10卷 / 03期
关键词：
bounded commutative Rl-monoid; general comparability property; Boolean element; State; State-morphism; extremal state; filter; maximal filter; MV-algebra; BL-algebra;
D O I：
10.1007/s00500-005-0473-0
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
Bounded commutative Rl-monoids are a generalization of MV-algebras as well as of BL-algebras. For such monoids the authors in [DvRa] introduced states, analogues of probability measures. We study Boolean elements and introduce the general comparability property. It entails that the monoids with the property are BL-algebras, and extremal states on Boolean elements can be uniquely extended to extremal states on the monoids. Moreover, the hull-kernel topology of maximal filters is totally disconnected.
引用
收藏
页码：212 / 218
页数：7
相关论文
共 24 条
  • [1] Varieties of BL-algebras I: general properties
    Agliano, P
    Montagna, F
    [J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2003, 181 (2-3) : 105 - 129
  • [2] Cancellative residuated lattices
    Bahls, P
    Cole, J
    Galatos, N
    Jipsen, P
    Tsinakis, C
    [J]. ALGEBRA UNIVERSALIS, 2003, 50 (01) : 83 - 106
  • [3] The structure of residuated lattices
    Blount, K
    Tsinakis, C
    [J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2003, 13 (04) : 437 - 461
  • [4] Chang C. C., 1958, Trans. Amer. Math. Soc., V88, P467, DOI DOI 10.1090/S0002-9947-1958-0094302-9
  • [5] Basic Fuzzy Logic is the logic of continuous t-norms and their residua
    R. Cignoli
    F. Esteva
    L. Godo
    A. Torrens
    [J]. Soft Computing, 2000, 4 (2) : 106 - 112
  • [6] Cignoli R., 1991, STUDIA LOGICA, V50, P375
  • [7] Finite BL-algebras
    Di Nola, A
    Lettieri, A
    [J]. DISCRETE MATHEMATICS, 2003, 269 (1-3) : 93 - 112
  • [8] Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras
    Dvurecenskij, A
    [J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2003, 74 : 121 - 143
  • [9] Dvurecenskij A., 2000, MATH ITS APPL, V516
  • [10] DVURECENSKIJ A, UNPUB PROBABILISTIC
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