We propose an internal calculus to check the satisfiability of a set of formulas in ${\boldsymbol {S4}}$. Our calculus directly supports model extraction and is designed so to implement a forward proof-search strategy that can be understood as a top-down construction of a model. We prove that the extracted models have minimal height.

中文翻译：

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S4中模型生成的前向内部演算

我们提出了一种内部演算来检查 ${\boldsymbol {S4}}$ 中一组公式的可满足性。我们的演算直接支持模型提取，旨在实现前向证明搜索策略，可以理解为模型的自上而下构造。我们证明提取的模型具有最小的高度。