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Despite being fairly powerful, finite non-deterministic matrices are unableto characterize some logics of formal inconsistency, such as those foundbetween $\textbf{mbCcl}$ and $\textbf{Cila}$. In order to overcome thislimitation, we propose here restricted non-deterministic matrices (in short,RNmatrices), which are non-deterministic algebras together with a subset of theset 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 anovel decision procedure for these logics. Moreover, we show that the RNmatrixsemantics proposed here induces naturally a labelled tableau system for each$C_n$, which constitutes another decision procedure for these logics. This newsemantics allows us to conceive da Costa's hierarchy of $C$-systems as a familyof (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 $C_n$.

A simple decision procedure for da Costa's Cn logics by Restricted Nmatrix semantics