标题： 模态扩展中格性质的表征 显示英文标题

标题： Characterization of Lattice Properties Within Modal Extensions

摘要： 本文研究了基于格的逻辑向模态语言的扩展。 我们注意到，这种扩展有多种方法，因为必然性算子的解释不由底层格结构唯一确定。 最自然的解释将必然性定义为在所有可达世界中公式真值的交集——我们称之为\textitnormal 解释。 我们考察了在这种和其他解释下出现的逻辑性质，包括结果模态逻辑满足公理K和其他常见模态有效性条件的情况。 此外，我们考虑了必然性仅归因于在所有可达世界中成立的公式的情况。 显示英文摘要

摘要： This paper investigates the extension of lattice-based logics into modal languages. We observe that such extensions admit multiple approaches, as the interpretation of the necessity operator is not uniquely determined by the underlying lattice structure. The most natural interpretation defines necessity as the meet of the truth values of a formula across all accessible worlds -- an approach we refer to as the \textitnormal interpretation. We examine the logical properties that emerge under this and other interpretations, including the conditions under which the resulting modal logic satisfies the axiom K and other common modal validities. Furthermore, we consider cases in which necessity is attributed exclusively to formulas that hold in all accessible worlds.