Reasoning with Time Intervals: A Logical and Computational Perspective

Table 1

Allen’s interval relations, excluding equality.

[𝑎,𝑏]𝑚[𝑐,𝑑]⇔𝑏=𝑐
[𝑎,𝑏]𝑏[𝑐,𝑑]⇔𝑏<𝑐
[𝑐,𝑑]𝑠[𝑎,𝑏]⇔𝑎=𝑐,𝑑<𝑏
[𝑐,𝑑]𝑓[𝑎,𝑏]⇔𝑏=𝑑,𝑎<𝑐
[𝑐,𝑑]𝑑[𝑎,𝑏]⇔𝑎<𝑐,𝑑<𝑏
[𝑎,𝑏]𝑜[𝑐,𝑑]⇔𝑎<𝑐<𝑏<𝑑