The paper introduces an interval-based temporal logic for representing and reasoning about temporal knowledge. It proposes a system that uses temporal intervals as primitive elements and employs constraint propagation to manage relationships between intervals. The system allows for precise control over the amount of deduction performed, making it suitable for applications involving relative temporal information that cannot be described by absolute dates. The system is designed to handle the complexity of temporal reasoning in artificial intelligence, including tasks such as modeling processes, maintaining historical data, and managing interactive systems where the present moment is continually updated. The paper discusses various approaches to temporal representation, including state space approaches, date line systems, before/after chaining, and formal models. It argues that interval-based systems are more expressive and computationally feasible than point-based systems, as they can capture relative temporal relationships that are not expressible in date-based systems. The system described in the paper uses a network of intervals, where each interval is connected to others through relationships defined by constraint propagation. This allows for efficient reasoning about temporal relationships, including during, before, after, and overlapping intervals. The system introduces the concept of reference intervals, which are used to group intervals into clusters where the temporal constraints between each pair of intervals in the cluster are fully computed. This reduces the space requirements of the system while maintaining its inferential power. Reference intervals allow for efficient retrieval of temporal relationships by enabling the system to search through a hierarchy of intervals, rather than propagating constraints across all intervals in the network. The paper also discusses the representation of the present moment, which is modeled as a variable that can be updated without requiring a complete reorganization of the database. This is achieved by using reference intervals to control the inferences resulting from updating the present moment. The system is implemented and used in various applications, including natural language processing, process modeling, and automatic problem-solving systems. The system is also extended to include reasoning about durations and dates, allowing for more complex temporal reasoning tasks.The paper introduces an interval-based temporal logic for representing and reasoning about temporal knowledge. It proposes a system that uses temporal intervals as primitive elements and employs constraint propagation to manage relationships between intervals. The system allows for precise control over the amount of deduction performed, making it suitable for applications involving relative temporal information that cannot be described by absolute dates. The system is designed to handle the complexity of temporal reasoning in artificial intelligence, including tasks such as modeling processes, maintaining historical data, and managing interactive systems where the present moment is continually updated. The paper discusses various approaches to temporal representation, including state space approaches, date line systems, before/after chaining, and formal models. It argues that interval-based systems are more expressive and computationally feasible than point-based systems, as they can capture relative temporal relationships that are not expressible in date-based systems. The system described in the paper uses a network of intervals, where each interval is connected to others through relationships defined by constraint propagation. This allows for efficient reasoning about temporal relationships, including during, before, after, and overlapping intervals. The system introduces the concept of reference intervals, which are used to group intervals into clusters where the temporal constraints between each pair of intervals in the cluster are fully computed. This reduces the space requirements of the system while maintaining its inferential power. Reference intervals allow for efficient retrieval of temporal relationships by enabling the system to search through a hierarchy of intervals, rather than propagating constraints across all intervals in the network. The paper also discusses the representation of the present moment, which is modeled as a variable that can be updated without requiring a complete reorganization of the database. This is achieved by using reference intervals to control the inferences resulting from updating the present moment. The system is implemented and used in various applications, including natural language processing, process modeling, and automatic problem-solving systems. The system is also extended to include reasoning about durations and dates, allowing for more complex temporal reasoning tasks.