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## Hierarchical Arc Consistency for Disjoint Real Intervals in Constraint Logic Programming (1992)

Venue: | COMPUTATIONAL INTELLIGENCE |

Citations: | 19 - 0 self |

### Citations

2939 | Maintaining knowledge about temporal intervals
- Allen
- 1983
(Show Context)
Citation Context ...e inequality is useful in temporal and spatial reasoning problems. For instance, Figure 2 gives an Echidna program for scheduling tasks using some of the relations on temporal intervals described in (=-=Allen, 1983-=-). A task is represented by a term task(S, D) where S is the start time of the task and D is the duration of the task. The predicate, in(Task, SuperTask), is true if the interval for SuperTask contain... |

2080 |
Foundations of Logic Programming
- Lloyd
- 1984
(Show Context)
Citation Context ...f the paper is organized as follows: Section 2 describes how Echidna augments a logic programming language with real number constraints. Section 3 briefly describes the SLD-resolution theorem prover (=-=Lloyd, 1984-=-) and arc consistency algorithms (Mackworth, 1977) used in Echidna. Section 4 specifies Echidna's adaptation of hierarchical arc consistency (Mackworth, et al., 1985) for real number constraints. Sect... |

1150 |
Consistency in networks of relations
- Mackworth
- 1977
(Show Context)
Citation Context ...y exponential time complexity in the worst case (Buchberger, 1985). The CHIP CLP language (Van Hentenryck, 1989) and BNR Prolog (Older and Vellino, 1990) use consistency and case analysis algorithms (=-=Mackworth, 1977-=-) for solving constraints. Consistency algorithms require that variables be associated with domains which are sets of candidate values for a variable. For consistency algorithms, a domain must be repr... |

660 | Concrete Mathematics
- Graham, Knuth, et al.
- 1989
(Show Context)
Citation Context ...y) is open while the other is closed. There are several reasonable definitions for mid(x,y). If an unbounded precision (eg. rational) number system is used, then the mean ((x+y)/2) or the mediant 13 (=-=Graham et al., 1989-=-) can be used. If a floating point number system is used, then the number nearest to the mean or the median number in the system between x and y can be used. Cleary (1987) studies the efficiency of th... |

606 | Introduction to Interval Computations - Alefeld, Herzberger - 1983 |

426 | Constraint Satisfaction in Logic Programming - Hentenryck - 1989 |

307 |
An introduction to Prolog-III.
- Colmerauer
- 1990
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Citation Context ...on There have been many proposals for adding sound implementations of numeric processing to Prolog. Constraint logic programming (CLP) languages like CLP(IR) (Jaffar and Michaylov, 1987), Prolog III (=-=Colmerauer, 1990-=-), and CAL (Aiba et al., 1988) use symbolic constraint solving techniques. However, CLP(IR) and Prolog III can only actively process 1 linear constraints using linear programming algorithms. CAL activ... |

295 |
The Complexity of Some Polynomial Network Consistency Algorithms for Constraint Satisfaction Problems.
- Mackworth, Freuder
- 1985
(Show Context)
Citation Context ... algorithms can be very expensive when domain sizes are large. For instance, the running time of AC-3 is proportional to the square of the domain size in the best case and the cube in the worst case (=-=Mackworth & Freuder, 1985-=-). An extensional representation for real domains is impossible. Instead, we introduce a hierarchical and intensional domain representation. HACR is based on the hierarchical arc consistency algorithm... |

258 |
Synthesizing constraint expressions,”
- Freuder
- 1978
(Show Context)
Citation Context ...tions in the CSP. Arc consistency algorithms only consider constraints in isolation. Higher levels of consistency can be achieved using path consistency and k-consistency algorithms (Mackworth, 1977; =-=Freuder, 1978-=-), but these general algorithms cannot compete with specialized algorithms for linear constraints. 5.4 Scheduling Given the scheduling program introduced earlier in Figure 2, consider the query: [39] ... |

252 |
Constraint propagation with interval labels
- Davis
- 1987
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Citation Context ...variable domains (the "label language") and constraints (the "constraint language"). Echidna implements label and constraint languages which are more general than the real number s=-=ystems surveyed in (Davis, 1987-=-) and Echidna's label language is more general than BNR Prolog's. Our label language is a collection of disjoint real interval sets and it contains real intervals as a subset. This makes it possible f... |

227 |
The art of Prolog: advanced programming techniques.”
- Sterling, Shapiro
- 1986
(Show Context)
Citation Context ...cerned with real number processing. For a description of other aspects of the language, see (Havens, et al., 1990) and (Havens, 1991). In this presentation, we augment the syntax of Edinburgh Prolog (=-=Sterling and Shapiro, 1986-=-) as necessary for exposition. Echidna provides domain constraints, equalities, inequalities, and disjunctions of inequalities on real numeric expressions. A domain constraint is a unary constraint of... |

127 |
Constraint Satisfaction Algorithms,
- Nadel
- 1989
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Citation Context ...ctions. Unlike BNR Prolog, our algorithms also support disjunctions of inequalities as atomic constraints. Echidna handles such general systems of constraints by using partial consistency algorithms (=-=Nadel, 1989-=-). Partial consistency algorithms approximate the set of solutions to a constraint satisfaction problem (CSP) by computing a superset of the solutions. Good partial consistency algorithms compute a su... |

84 |
Methodology and implementation of a CLP system
- Jaffar, Michaylov
- 1987
(Show Context)
Citation Context ...ls Minor: Theorem Proving 3 1. Introduction There have been many proposals for adding sound implementations of numeric processing to Prolog. Constraint logic programming (CLP) languages like CLP(IR) (=-=Jaffar and Michaylov, 1987-=-), Prolog III (Colmerauer, 1990), and CAL (Aiba et al., 1988) use symbolic constraint solving techniques. However, CLP(IR) and Prolog III can only actively process 1 linear constraints using linear pr... |

82 |
Computer Methods for the Range of Functions
- Ratschek, Rokne
- 1984
(Show Context)
Citation Context ...ange(f E ) and max range(f E ), can be calculated from the respective minima and maxima of the function arguments by analyzing the monotonicity and continuity properties of the function (Bundy, 1984; =-=Ratschek and Rokne, 1984-=-). This analysis is applied in Echidna for the arithmetic, exponential, logarithmic, root extraction, and trigonometric functions. 4.4.1 Equalities For simple equalities of the form iso(T, C) = `T = E... |

59 |
Gréobner Bases: An Algorithmic Method
- Buchberger
- 1985
(Show Context)
Citation Context ...aints using linear programming algorithms. CAL actively processes polynomial constraints using algorithms from polynomial ideal theory which have doubly exponential time complexity in the worst case (=-=Buchberger, 1985-=-). The CHIP CLP language (Van Hentenryck, 1989) and BNR Prolog (Older and Vellino, 1990) use consistency and case analysis algorithms (Mackworth, 1977) for solving constraints. Consistency algorithms ... |

55 | Extending prolog with constraint arithmetics on real intervals
- Older, Vellino
- 1990
(Show Context)
Citation Context ...straints using algorithms from polynomial ideal theory which have doubly exponential time complexity in the worst case (Buchberger, 1985). The CHIP CLP language (Van Hentenryck, 1989) and BNR Prolog (=-=Older and Vellino, 1990-=-) use consistency and case analysis algorithms (Mackworth, 1977) for solving constraints. Consistency algorithms require that variables be associated with domains which are sets of candidate values fo... |

44 | An efficient arc consistency algorithm for a class of CSP problems - Deville, Hentenryck - 1991 |

33 |
Hierarchical arc consistency: exploiting structured domains in constraint satisfaction problems,
- Mackworth, Mulder, et al.
- 1985
(Show Context)
Citation Context ...y describes the SLD-resolution theorem prover (Lloyd, 1984) and arc consistency algorithms (Mackworth, 1977) used in Echidna. Section 4 specifies Echidna's adaptation of hierarchical arc consistency (=-=Mackworth, et al., 1985-=-) for real number constraints. Section 5 gives some sample runs using Echidna (version 1.0) and compares it with other CLP languages. Finally, Section 6 draws some conclusions about this research. 2. ... |

31 | Negation and Control in Prolog - Naish - 1986 |

25 |
Constraint logic programming language CAL
- Aiba, Sakai, et al.
- 1988
(Show Context)
Citation Context ...osals for adding sound implementations of numeric processing to Prolog. Constraint logic programming (CLP) languages like CLP(IR) (Jaffar and Michaylov, 1987), Prolog III (Colmerauer, 1990), and CAL (=-=Aiba et al., 1988-=-) use symbolic constraint solving techniques. However, CLP(IR) and Prolog III can only actively process 1 linear constraints using linear programming algorithms. CAL actively processes polynomial cons... |

8 |
Echidna Constraint Reasoning System: Next-generation Expert System Technology
- HAVENS, SIDEBOTTOM, et al.
- 1990
(Show Context)
Citation Context ...aints is missed although sometimes answers contain no solutions. This paper describes an approach to real number constraint processing which has been implemented in a new CLP language called Echidna (=-=Havens, et al., 1990-=-; Havens, 1991). Like both CHIP and BNR Prolog, Echidna uses consistency algorithms which can actively 1 By active constraint processing, we mean using constraints to at least partially test their sat... |

2 |
A Generalized Interval Package and Its Use for Semantic Checking
- Bundy
- 1984
(Show Context)
Citation Context ...bounds, min range(f E ) and max range(f E ), can be calculated from the respective minima and maxima of the function arguments by analyzing the monotonicity and continuity properties of the function (=-=Bundy, 1984-=-; Ratschek and Rokne, 1984). This analysis is applied in Echidna for the arithmetic, exponential, logarithmic, root extraction, and trigonometric functions. 4.4.1 Equalities For simple equalities of t... |

2 |
Dataflow Dependency Backtracking in a New CLP Language
- Havens
- 1991
(Show Context)
Citation Context ...gh sometimes answers contain no solutions. This paper describes an approach to real number constraint processing which has been implemented in a new CLP language called Echidna (Havens, et al., 1990; =-=Havens, 1991-=-). Like both CHIP and BNR Prolog, Echidna uses consistency algorithms which can actively 1 By active constraint processing, we mean using constraints to at least partially test their satisfiability wh... |

1 | An Intelligent Basis for Design - Calvert, Dickinson, et al. - 1991 |

1 |
Projection of Numeric Constraints with Interval Domains
- Sidebottom
- 1992
(Show Context)
Citation Context ...rivial for constraints involving only invertible functions. A full presentation of how to compute projections of constraints involving more functions with open and closed intervals is in preparation (=-=Sidebottom, 1992-=-). We consider here only computing p T (C) for an arbitrary constraint C subject to these two restrictions. Echidna satisfies restriction 2 by introducing intermediate variables to decompose complex c... |