论文标题
有条件的逻辑已完成，以实现飞机中的凸度
Conditional Logic is Complete for Convexity in the Plane
论文作者
论文摘要
我们证明了优先条件逻辑相对于欧几里得平面中有限点的凸度的完整性。如果设置的所有极端点解释前面的点满足随之而来的，则有条件的定义是在有限的点中真实的。同等地，如果先决条件包含在满足先例和随之而来的点的凸壳中，则条件是正确的。然后，我们的结果是，每个没有嵌套条件的一致公式在基于平面中有限点的模型中都可以满足。证明依赖于里奇特（Richter）和罗杰斯（Rogers）的结果表明，每个有限的抽象凸几何形状都可以由平面中的凸多边形表示。
We prove completeness of preferential conditional logic with respect to convexity over finite sets of points in the Euclidean plane. A conditional is defined to be true in a finite set of points if all extreme points of the set interpreting the antecedent satisfy the consequent. Equivalently, a conditional is true if the antecedent is contained in the convex hull of the points that satisfy both the antecedent and consequent. Our result is then that every consistent formula without nested conditionals is satisfiable in a model based on a finite set of points in the plane. The proof relies on a result by Richter and Rogers showing that every finite abstract convex geometry can be represented by convex polygons in the plane.
