BOCHVAR'S THREE-VALUED LOGIC AND LITERAL PARALOGICS: Their Lattice and Functional Equivalence
BOCHVAR'S THREE-VALUED LOGIC AND LITERAL PARALOGICS: Their Lattice and Functional Equivalence
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DOI：
10.12775/llp.2016.029
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发表时间：
2017-06-01
影响因子：
0.5
通讯作者：
Tomova, Natalya
中科院分区：
文献类型：
--
作者：
Karpenko, Alexander;Tomova, Natalya
本文讨论命题字面类比逻辑的各种特征。字面拟逻辑是这样一种逻辑，在该逻辑中，仿相容、仿完备和超正规等准性质仅在字面层面上出现；即，公式是命题字母或其迭代否定。我们首先分析Bochvars三值无义逻辑B-3，它包括命题经典逻辑CPC的两个同构。这两个强同构的组合导致了两个功能等价的著名的类比逻辑P-1和I-1的构造。此外，这些逻辑中的每一个在功能上都等同于仅由外部公式组成的逻辑B-3的片段。综上所述，我们构造了一个关于准性质占有的三值拟逻辑的四元素格。
In the present paper, various features of the class of propositional literal paralogics are considered. Literal paralogics are logics in which the paraproperties such as paraconsistence, paracompleteness and paranormality, occur only at the level of literals; that is, formulas that are propositional letters or their iterated negations. We begin by analyzing Bochvars three-valued nonsense logic B-3 , which includes two isomorphs of the propositional classical logic CPC. The combination of these two strong isomorphs leads to the construction of two famous paralogics P-1 and I-1, which are functionally equivalent. Moreover, each of these logics is functionally equivalent to the fragment of logic B-3 consisting of external formulas only. In conclusion, we structure a four-element lattice of three-valued paralogics with respect to the possession of paraproperties.