Allen's intervals, or Allen relations, are a fundamental mathematical framework for representing and reasoning about time in artificial intelligence. Proposed by James F. Allen in 1983, this approach precisely defines the possible qualitative relationships between two temporal intervals. It distinguishes thirteen basic relations such as "precedes," "overlaps," "starts," and "finishes," enabling the modeling of complex temporal scenarios. This fine granularity sets it apart from other temporal models, such as pure time points or simple start/end markers. Allen's intervals are foundational for temporal inference, automated planning, and the analysis of event sequences.
Use cases and examples
Allen's intervals are used in task planning, intelligent calendar management, story understanding, computational biology (e.g., for studying the order of gene expression), and temporal reasoning in embedded systems. For instance, a personal assistant may use these relations to ensure that one appointment does not overlap with another or to deduce potential conflicts in a complex schedule.
Main software tools, libraries, frameworks
Several software libraries handle Allen's intervals: PyInterval (Python), AllenIntervalAlgebra (Java), as well as modules in planning frameworks like PDDL or the Temporal Logic of Actions. Tools such as AllenAI or the CSP solver Gecode also support reasoning over temporal intervals.
Recent developments, evolutions, and trends
Recent research focuses on integrating Allen's intervals with probabilistic models and extending them to multivariate or uncertain scenarios (temporal uncertainty). Their use in machine learning, particularly for sequence analysis (NLP, bioinformatics) or adaptive planning in robotics, is growing rapidly. Recent work also aims to optimize the scalability of reasoning algorithms to handle very large sets of intervals in real time.