The mathematics of inheritance systems
The mathematics of inheritance systems
Principles of artificial intelligence
Principles of artificial intelligence
Maintaining knowledge about temporal intervals
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Spatio-Temporal Reasoning and Linear Inequalitites
Spatio-Temporal Reasoning and Linear Inequalitites
Planning using a temporal world model
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
An investigation of opportunistic constraint satisfaction in space planning
IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 2
| Hi-index | 0.00 |
A popular representation of events and their relative alignment in time is James Allen's intervals and algebra. Networks of disjunctive interval constraints have served both to assimilate knowledge from ambiguous sentences, and to hold partial solutions in a planner. The satisfiability of these networks is of practical concern, and little has been achieved beyond proving that determining satisfiability is NP-hard. This paper scrutinizes the interval representation and its mechanisms. We make explicit the unstated assumptions of the mechanisms, introduce several useful theorems regarding interval networks, distinguish three types of inconsistency exhibited by these networks, and point out under what conditions these inconsistencies are detected. Finally the theorems, observations, and distinctions regarding inconsistency are exploited to design a practical algorithm to determine the satisfiability of an interval network. The extension of our results to two dimensional spatial reasoning is under investigation.