弱模态逻辑的闭包语义：完备性与表示
Closure Semantics for Weak Modal Logics: Completeness and Representations
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中文总结 AI 辅助
本文为弱模态逻辑引入闭包语义，证明其可靠性与强完备性，并给出与邻域、FMT及克里普克语义间的保真翻译。
中文摘要 AI 辅助
弱模态逻辑可以通过限制控制模态算子的公理和推理规则来获得。在极端情况下，可以考虑最小模态逻辑，其中不施加任何特定的模态公理或推理规则。我们引入了闭包语义，一种针对此类弱模态逻辑的新可能世界语义，并建立了一系列系统的可靠性和强完备性。我们还给出了闭包模型与其他可能世界语义（包括邻域、FMT和克里普克语义）之间的保真翻译。
英文摘要
Weak modal logics can be obtained by restricting the axioms and inference rules governing the modal operator. At the extreme, one may consider the least modal logic, in which no specifically modal axiom or inference rule is imposed. We introduce closure semantics, a new possible-world semantics for such weak modal logics, and establish soundness and strong completeness for a range of systems. We also give truth-preserving translations between closure models and other possible-world semantics, including neighborhood, FMT, and Kripke semantics.
