# Revising Hull and Box Consistency

@inproceedings{Benhamou1999RevisingHA, title={Revising Hull and Box Consistency}, author={Fr{\'e}d{\'e}ric Benhamou and Fr{\'e}d{\'e}ric Goualard and Laurent Granvilliers and Jean-François Puget}, booktitle={ICLP}, year={1999} }

Most interval-based solvers in the constraint logic programming framework are based on either hull consistency or box consistency (or a variation of these ones) to narrow domains of variables involved in continuous constraint systems. This paper first presents HC4, an algorithm to enforce hull consistency without decomposing complex constraints into primitives. Next, an extended definition for box consistency is given and the resulting consistency is shown to subsume hull consistency. Finally…

## 404 Citations

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## References

SHOWING 1-10 OF 14 REFERENCES

### Interval Constraint Logic Programming

- Computer Science, MathematicsConstraint Programming
- 1994

An overview on the use of interval arithmetic to process numerical constraints in Constraint Logic Programming, and the description of the general framework based on approximations, on its application to interval constraint solving over continuous and discrete quantities is presented.

### CLP(Intervals) Revisited

- Computer ScienceILPS
- 1994

Experimental results indicate that Newton outperforms existing languages by an order of magnitude and is competitive with some state-of-the-art tools on some standard benchmarks.

### An Extension of the WAM for Hybrid Interval Solvers

- Computer ScienceJ. Funct. Log. Program.
- 1999

The extension of the WAM instruction set necessary to support the new features of DecLIC is described, along with the new internal structures, and benchmark comparisons show that combination permits, on certain cases, relevant speed-ups in the resolution process.

### A C++ implementation of CLP

- Computer Science
- 1997

A C++ library that embodies Constraint Logic Programming (CLP) concepts such as logical variables, incremental constraint satisfaction and backtracking, and which combines Object Oriented Programming (OOP) with CLP.

### Applying Interval Arithmetic to Real, Integer, and Boolean Constraints

- Computer ScienceJ. Log. Program.
- 1997

### Comparing Partial Consistencies

- Computer ScienceReliab. Comput.
- 1999

The relations among the different partial consistencies which are main emphasis of these algorithms are stated and the capability of these partial consistency to handle the so-called dependency problem is analysed.

### Constraint Arithmetic on Real Intervals

- Computer ScienceWCLP
- 1991

Constraint interval arithmetic is a sublanguage of BNR Prolog which takes a new approach to the old problem of deriving numerical consequences from algebraic models by bypassing the traditional dichotomy between (numeric) calculation and (symbolic) proofs.

### On automatic differentiation

- Environmental Science
- 1988

Simulation of the radionucleide transport in underground in order to determine the impact of a possible propagation of radioelements and the modelling of the flow in porous media around the storage requires to know the physical parameters of the different geological layers.