| 模糊模态逻辑系统MLuk中的可达广义重言式 |
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| 引用本文： | 邹尚田,王国俊. 模糊模态逻辑系统MLuk中的可达广义重言式[J]. 山东大学学报(自然科学版), 2009, 0(8): 80-85 |
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| 作者姓名： | 邹尚田 王国俊 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安710062 |
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| 基金项目： | 国家自然科学基金资助项目（10771129） |
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| 摘 要： | 将赋值格取为单位区间并将二元关系R模糊化，研究了模糊模态逻辑系统MLuk，然后将其赋值格离散化研究了多值模态逻辑系统MLn；证明了在MLn中，对任一可能的赋值α都存在可达α-重言式；在MLuk中对任一有理数α∈[0，1]都存在可达α-重言式；指出了在风系统R0起关键作用的升级算法对MLn系统已不再适用，并分析了其原因。
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| 关 键 词： | 模糊模态逻辑 模糊模态逻辑系统MLuk 可达广义重言式 可达广义矛盾式 类类不空定理 |
Exact generalized tautologies in fuzzy modal logic system MLuk |
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| ZOU Shang-tian,WANG Guo-jun. Exact generalized tautologies in fuzzy modal logic system MLuk[J]. Journal of Shandong University(Natural Science Edition), 2009, 0(8): 80-85 |
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| Authors: | ZOU Shang-tian WANG Guo-jun |
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| Affiliation: | (College of Mathematics and Information Science, Shaanxi Normal University, Xi＇an 710062, Shaanxi, China) |
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| Abstract: | The fuzzy modal logic system MLuk is introduced, where the evaluation lattice is taken to be the unite interval and the binary relation R is fuzzified, then it is discretized to be the multi-valued fuzzy modal logic system MLn. It is proved that for any possible value α in MLn there exists an exact α-tautology; and in MLuk, for any rational α ∈ [ 0,1 ], there exists an exact α-tautology. It is pointed out that the lift-algorithm which plays a key role in Ro systems is not suitable for the system MLn, and the reasons are analyzed. |
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| Keywords: | fuzzy modal logic fuzzy modal logic system MLuk exact generalized tautologies exact generalized contradictions univerisal theorem |
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