Strong non-standard completeness for fuzzy logics
Strong non-standard completeness for fuzzy logics
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DOI：
10.1007/s00500-007-0184-9
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发表时间：
2008-02
期刊：
影响因子：
4.1
通讯作者：
T. Flaminio
中科院分区：
文献类型：
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作者：
T. Flaminio
本文引入模糊逻辑的强非标准完备性概念。这个概念自然地产生于著名的超积构造。粗略地说，对数强非标准完备是指，对任意可数理论Γ和任意公式φ使得，存在一个公式到a-代数的求值，使得的论域是真实的单位区间[0，1]的非阿基米德扩张，e是Γ的模型，布特（φ）< 1。然后，我们将应用SNSC证明，各种模态模糊逻辑允许处理简单的和条件概率的无限值事件是完整的关于类的模型定义从非标准措施，即措施采取价值。
In this paper we are going to introduce the notion ofstrong non-standard completeness(SNSC) for fuzzy logics. This notion naturally arises from the well known construction by ultraproduct. Roughly speaking, to say that a logicis strong non-standard complete means that, for any countable theory Γ overand any formulaφsuch that, there exists an evaluationeof-formulas into a-algebrasuch that the universe ofis a non-Archimedean extensionof the real unit interval [0,1],eis a model for Γ, bute(φ) < 1. Then we will apply SNSC to prove that various modal fuzzy logics allowing to deal with simple and conditional probability of infinite-valued events are complete with respect to classes of models defined starting from non-standard measures, that is measures taking value in.