While the paths humans take play out in social as well as physical space, measures to describe and compare their trajectories are carried out in abstract, typically Euclidean, space. When these measures are applied to trajectories of actual individuals in an application area, alterations that are inconsequential in abstract space may suddenly become problematic once overlaid with geographic reality. In this work, we present a different view on trajectory similarity by introducing a measure that utilizes logical entailment. This is an inferential perspective that considers facts as triple statements deduced from the social and environmental context in which the travel takes place, and their practical implications. We suggest a formalization of entailment-based trajectory similarity, measured as the overlapping proportion of facts, which are spatial relation statements in our case study. With the proposed measure, we evaluate LSTM-TrajGAN, a privacy-preserving trajectory-generation model. The entailment-based model evaluation reveals potential consequences of disregarding the rich structure of geographic space (e.g., miscalculated insurance risk due to regional shifts in our toy example). Our work highlights the advantage of applying logical entailment to trajectory-similarity reasoning for location-privacy protection and beyond.

翻译：虽然人类行走的路径同时展现在社会空间与物理空间中，用于描述和比较这些轨迹的度量方法却始终在抽象空间（通常为欧几里得空间）中进行。当这些度量方法应用于真实个体的轨迹数据时，那些在抽象空间中无足轻重的变化，一旦叠加上地理现实，就可能骤然引发问题。本研究通过引入一种利用逻辑蕴涵的度量方法，提出关于轨迹相似性的新视角。这是一种推理性的视角，将事实视为从出行发生的社会与环境背景中推导出的三元组陈述，并关注其实际影响。我们提出了基于蕴涵的轨迹相似性形式化定义，以事实（在本案例研究中指空间关系陈述）的重叠比例进行度量。利用该度量方法，我们对隐私保护轨迹生成模型LSTM-TrajGAN进行了评估。基于蕴涵的模型评估揭示了忽视地理空间丰富结构可能带来的潜在后果（例如，在玩具示例中因区域偏移导致的保险风险计算错误）。本研究凸显了将逻辑蕴涵应用于轨迹相似性推理对位置隐私保护及其拓展领域的重要意义。