A Few More Useful 8-valued Logics for Reasoning with Tetralattice EIGHT4
A Few More Useful 8-valued Logics for Reasoning with Tetralattice EIGHT4
复制标题
一些更有用的 8 值逻辑，用于 Tetralattice EIGHT4 推理
DOI：
10.1007/s11225-009-9198-x
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发表时间：
2009
期刊：
影响因子：
0.7
通讯作者：
D. Zaitsev
中科院分区：
文献类型：
--
作者：
D. Zaitsev
在计算机网络的有用逻辑中，Shramko 和 Wansing 将 Belnap 4 值逻辑的初始值推广到集合 16，作为 Belnap 4 的幂集。这种推广产生了一个非常具体的代数结构——具有三种排序的三格 SIXTEEN3：信息、真值和假值。在本文中，提出了一种略有不同的概括方式。作为进一步泛化的基础，选择集合 3，其中初始值为 a — 传入数据被断言，d — 传入数据被拒绝，u — 传入数据既不断言也不被拒绝，对应于答案“不知道”。这样做时，考虑 3 的幂集，即集合 8。事实证明，在构成四格子 EIGHT4 的集合 8 上自然定义的不是三个而是四个排序。除了上述三种排序关系之外，它是一种额外的不确定性排序。可以预见的是，a 阶（真值阶）和 d 阶（假阶）生成的逻辑与一级蕴涵一致。最后考虑具有两种操作（a-连接词和d-连接词）的逻辑以及通过a-排序定义的结果关系。提出了该逻辑的充分公理化。
In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is asserted, d — incoming data is denied, and u — incoming data is neither asserted nor denied, that corresponds to the answer “don’t know”. In so doing, the power-set of 3, that is the set 8 is considered. It turns out that there are not three but four orderings naturally defined on the set 8 that form the tetralattice EIGHT4. Besides three ordering relations mentioned above it is an extra uncertainty ordering. Quite predictably, the logics generated by a–order (truth order) and d–order (falsity order) coincide with first-degree entailment. Finally logic with two kinds of operations (a–connectives and d–connectives) and consequence relation defined via a–ordering is considered. An adequate axiomatization for this logic is proposed.