一句话：对点-区间二排序一阶时序语言的子语言按相对表达能力进行完整分类，澄清点是否应纳入区间语义。
时间本体与推理长期存在基于点和基于区间两类方法。区间方法通常把点当作零长度区间，而 Balbiani、Goranko 与 Sciavicco 近来提出两排序点-区间框架，使点和区间在形式话语中地位平等并可切换视角。本文研究基于同一原则的两排序一阶语言，其中包含点之间、区间之间以及跨排序的关系，这些关系可追溯至 Reich 等人的工作。作者对这类语言的子语言按相对表达能力给出完整分类，厘清在二排序一阶逻辑上加入一个或多个此类关系时，究竟有多少种、以及哪些是本质上不同的扩展。该结果从根本上处理了区间语义中是否应包含点的经典争议。
There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as a particular case of duration-less intervals. A recent result by Balbiani, Goranko, and Sciavicco presented an explicit two-sorted point-interval temporal framework in which time instants (points) and time periods (intervals) are considered on a par, allowing the perspective to shift between these within the formal discourse. We consider here two-sorted first-order languages based on the same principle, and therefore including relations, as first studied by Reich, among others, between points, between intervals, and inter-sort. We give complete classifications of its sub-languages in terms of relative expressive power, thus determining how many, and which, are the intrinsically different extensions of two-sorted first-order logic with one or more such relations. This approach roots out the classical problem of whether or not points should be included in a interval-based semantics.
@article{paperbot400,
title = {An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part I)},
author = {Willem Conradie and Salih Durhan and Guido Sciavicco},
journal = {Logical Methods in Computer Science},
volume = {Volume 14, Issue 2},
year = {2018},
doi = {10.23638/lmcs-14(2:15)2018}
}