The knotting probability of an arc diagram is defined as the quadruplet of four kinds of finner knotting probabilities which are invariant under a reasonable deformation containing an isomorphism on an arc diagram. In a separated paper, it is shown that every oriented spatial arc admits four kinds of unique arc diagrams up to isomorphisms determined from the spatial arc and the projection, so that the knotting probability of a spatial arc is defined. The definition of the knotting probability of an arc diagram uses the fact that every arc diagram induces a unique chord diagram representing a ribbon 2-knot. Then the knotting probability of an arc diagram is set to measure how many nontrivial ribbon genus 2 surface-knots occur from the chord diagram induced from the arc diagram. The conditions for an arc diagram with the knotting probability 0 and for an arc diagram with the knotting probability 1 are given together with some other properties and some examples.

中文翻译：

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弧形图的打结概率

弧形图的打结概率定义为在弧形图上包含同构的合理变形下不变的四种较细打结概率的四元组。在另一篇论文中，表明每个有向的空间弧都允许四种唯一的弧图，直到由空间弧和投影确定的同构，从而定义了空间弧的打结概率。弧形图的打结概率的定义使用了这样一个事实，即每个弧形图都会产生一个表示带状 2 结的唯一弦图。然后设置弧形图的打结概率来衡量从弧形图导出的弦图出现了多少非平凡的带属 2 表面结。