In the product $L_1\times L_2$ of two Kripke complete consistent logics, local tabularity of $L_1$ and $L_2$ is necessary for local tabularity of $L_1\times L_2$. However, it is not sufficient: the product of two locally tabular logics can be not locally tabular. We provide extra semantic and axiomatic conditions which give criteria of local tabularity of the product of two locally tabular logics. Then we apply them to identify new families of locally tabular products.

翻译：在两个克里普克完全且一致的逻辑的乘积 $L_1\times L_2$ 中，$L_1$ 与 $L_2$ 的局部表格化是 $L_1\times L_2$ 局部表格化的必要条件。然而，这并非充分条件：两个局部表格化逻辑的乘积可能不是局部表格化的。我们提出了额外的语义与公理化条件，为两个局部表格化逻辑乘积的局部表格性提供了判定准则。随后，我们应用这些准则识别出新的局部表格化乘积逻辑族。