Constraint propagation with interval labels
Artificial Intelligence
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Value Constraints in the CLP Scheme
Constraints
Constraint reasoning based on interval arithmetic
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
CLIP: A CLP(Intervals) Dialect for Metalevel Constraint Solving
PADL '00 Proceedings of the Second International Workshop on Practical Aspects of Declarative Languages
Spatial Inference - Learning vs. Constraint Solving
KI '02 Proceedings of the 25th Annual German Conference on AI: Advances in Artificial Intelligence
Safety verification of hybrid systems by constraint propagation based abstraction refinement
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
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We are concerned with interval constraints: solving constraints among real unknowns in such a way that soundness is not affected by rounding errors. The contraction operator for the constraint x + y = z can simply be expressed in terms of interval arithmetic. An attempt to use the analogous definition for x * y = z fails if the usual definitions of interval arithmetic are used. We propose an alternative to the interval arithmetic definition of interval division so that the two constraints can be handled in an analogous way. This leads to a unified treatment of both interval constraints and interval arithmetic that makes it easy to derive formulas for other constraint contraction operators. We present a theorem that justifies simulating interval arithmetic evaluation of complex expressions by means of constraint propagation. A naive implementation of this simulation is inefficient. We present a theorem that justifies what we call the totality optimization. It makes simulation of expression evaluation by means of constraint propagation as efficient as in interval arithmetic. It also speeds up the contraction operators for primitive constraints.