论文标题
DA Costa的CN逻辑的简单决策程序通过受限的NMATRIX语义
A simple decision procedure for da Costa's Cn logics by Restricted Nmatrix semantics
论文作者
论文摘要
尽管有限的非确定性矩阵无法表征一些正式不一致的逻辑，例如$ \ textbf {mbccl} $和$ \ textbf {cila} $之间的一些逻辑。为了克服这一限制，我们在这里提出了限制的非确定性矩阵（简而言之，rnmatrices），它们是非确定性代数以及一组估值集。这使我们不仅可以表征$ \ textbf {mbccl} $和$ \ textbf {cila} $（这等于等于语言，与da Costa的逻辑$ c_1 $），但DA Costa的整个层次结构是COSTA CACCULI $ C_N $。这为这些逻辑产生了新的决策程序。此外，我们表明，此处提出的RNMATRIX语义自然会为每个$ C_N $诱导一个标记的Tableau系统，这构成了这些逻辑的另一个决策过程。这种新的语义使我们能够构想Da Costa的$ c $系统层次结构（非确定性的）$（n+2）$ - 有价值的逻辑，其中$ n $是“不一致的真实”真实价值的数量，而2是“经典”或“一致的”真相“真相” $ C_N $。
Despite being fairly powerful, finite non-deterministic matrices are unable to characterize some logics of formal inconsistency, such as those found between $\textbf{mbCcl}$ and $\textbf{Cila}$. In order to overcome this limitation, we propose here restricted non-deterministic matrices (in short, RNmatrices), which are non-deterministic algebras together with a subset of the set of valuations. This allows us to characterize not only $\textbf{mbCcl}$ and $\textbf{Cila}$ (which is equivalent, up to language, to da Costa's logic $C_1$) but the whole hierarchy of da Costa's calculi $C_n$. This produces a novel decision procedure for these logics. Moreover, we show that the RNmatrix semantics proposed here induces naturally a labelled tableau system for each $C_n$, which constitutes another decision procedure for these logics. This new semantics allows us to conceive da Costa's hierarchy of $C$-systems as a family of (non deterministically) $(n+2)$-valued logics, where $n$ is the number of "inconsistently true" truth-values and 2 is the number of "classical" or "consistent" truth-values, for every $C_n$.
