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Kripke完备且一致的逻辑$L_1$与$L_2$的积$L_1\times L_2$中，$L_1$与$L_2$的局部表格性是$L_1\times L_2$局部表格性的必要条件。然而，该条件并不充分：两个局部表格逻辑的积可能不是局部表格的。我们给出额外的语义与公理条件，这些条件构成了两个局部表格逻辑之积局部表格性的判定准则。进而应用这些准则，识别出新的局部表格积族。