Falsification-aware (hyper)sequent calculi and Kripke semantics for normal modal logics including S4 and S5 are introduced and investigated in this study. These calculi and semantics are constructed based on the idea of a falsification-aware framework for Nelson’s constructive three-valued logic. The cut-elimination and completeness theorems for the proposed calculi and semantics are proved.

中文翻译：

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包括 S4 和 S5 在内的正态模态逻辑的证伪计算和语义

本研究介绍并研究了用于包括 S4 和 S5 在内的正常模态逻辑的证伪感知（超）序贯演算和 Kripke 语义。这些演算和语义是基于 Nelson 的建设性三值逻辑的证伪感知框架的思想构建的。证明了所提出的演算和语义的切割消除和完备性定理。