Hybrid logic is one of the extensions of modal logic. The many-dimensional product of hybrid logic is called hybrid product logic (HPL). We construct a sound and complete tableau calculus for two-dimensional HPL. Also, we made a tableau calculus for hybrid dependent product logic (HdPL), where one dimension depends on the other. In addition, we add a special rule to the tableau calculus for HdPL and show that it is still sound and complete. All of them lack termination, however.

翻译：混合逻辑是模态逻辑的一种扩展。混合逻辑的多维乘积被称为混合乘积逻辑（HPL）。我们为二维HPL构建了一个可靠且完备的Tableau演算。此外，我们还为混合依赖乘积逻辑（HdPL）构建了Tableau演算，其中一维依赖于另一维。进一步地，我们为HdPL的Tableau演算添加了一条特殊规则，并证明其仍保持可靠性和完备性。然而，所有这些演算均缺乏终止性。