In this study, falsification-aware semantics and sequent calculi for first-order classical logic are introduced and investigated. These semantics and sequent calculi are constructed based on a falsification-aware setting for first-order Nelson constructive three-valued logic (N3). In fact, these semantics and sequent calculi are regarded as those for a classical variant of N3 (i.e., a classical variant of N3 is identical to first-order classical logic). The completeness and cut-elimination theorems for the proposed semantics and sequent calculi are proved using Schütte’s method. Similar results for the propositional case are also obtained.

中文翻译：

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经典逻辑的证伪意识语义和顺序演算

在这项研究中，介绍和研究了一阶经典逻辑的证伪感知语义和后续演算。这些语义和后续演算是基于一阶纳尔逊构造三值逻辑 (N3) 的证伪感知设置构建的。事实上，这些语义和后续演算被视为N3的经典变体（即N3的经典变体与一阶经典逻辑相同）。使用 Schütte 方法证明了所提出的语义和后续演算的完备性和删减定理。对于命题案例也得到了类似的结果。