论文标题
Pledger的单分射线和椭圆飞机的模态逻辑的完整性
Completeness of Pledger's modal logics of one-sorted projective and elliptic planes
论文作者
论文摘要
肯·普雷德（Ken Pledger）使用支持命题模态逻辑模型的结构设计了平面几何形状的发生率关系的一级方法。他引入了一个模态系统12G，该系统在单分射线平面上有效，证明它具有许多非等效模态，并确定了其扩展的所有可能模式模式。这些扩展之一8F在椭圆飞机上是有效的。这些结果是在他的博士学位论文中提出的[14]，该论文已在《澳大利亚逻辑杂志》第1卷中转载。 18，不。 4。https：//doi.org/10.26686/ajl.v18i4.6831 在这里，我们表明12G和8F在其预期的一级几何解释中的有效性非常完整，并且具有有限的模型属性。这些证明应用了模态逻辑（典型模型，过滤）的标准技术，以及由YDE Venema介绍的逐步程序，用于构建两排射击平面。
Ken Pledger devised a one-sorted approach to the incidence relation of plane geometries, using structures that also support models of propositional modal logic. He introduced a modal system 12g that is valid in one-sorted projective planes, proved that it has finitely many non-equivalent modalities, and identified all possible modality patterns of its extensions. One of these extensions 8f is valid in elliptic planes. These results were presented in his doctoral dissertation [14], which has been reprinted in the Australasian Journal of Logic, vol. 18, no. 4. https://doi.org/10.26686/ajl.v18i4.6831 Here we show that 12g and 8f are strongly complete for validity in their intended one-sorted geometrical interpretations, and have the finite model property. The proofs apply standard technology of modal logic (canonical models, filtrations) together with a step-by-step procedure introduced by Yde Venema for constructing two-sorted projective planes.
