## Ordering Constraints over Feature Trees (1999)

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Citations: | 13 - 5 self |

### BibTeX

@MISC{Müller99orderingconstraints,

author = {Martin Müller and Joachim Niehren and Andreas Podelski},

title = {Ordering Constraints over Feature Trees},

year = {1999}

}

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### Abstract

Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular record descriptions. We introduce the constraint system FT of ordering constraints interpreted over feature trees. Under the view that feature trees represent symbolic information, the relation corresponds to the information ordering ("carries less information than"). We present two algorithms in cubic time, one for the satisfiability problem and one for the entailment problem of FT . We show that FT has the independence property. We are thus able to handle negative conjuncts via entailment and obtain a cubic algorithm that decides the satisfiability of conjunctions of positive and negated ordering constraints over feature trees. Furthermore, we reduce the satisfiability problem of Dorre's weak subsumption constraints to the satisfiability problem of FT and improve the complexity bound for solving weak subsumption constraints from O(n^5) to O(n³).

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Citation Context ...ability, entailment, complexity. 1 Introduction Feature constraints have been used for describing records in constraint programming [2, 24, 23] and record like structures in computational linguistics =-=[13, 12, 20, 18, 19]-=-. Following [3, 5, 4] we consider feature constraints as predicate logic formulae that are interpreted in the structure of feature trees. A feature tree is a possibly infinite tree with unordered labe... |

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Citation Context ...ability, entailment, complexity. 1 Introduction Feature constraints have been used for describing records in constraint programming [2, 24, 23] and record like structures in computational linguistics =-=[13, 12, 20, 18, 19]-=-. Following [3, 5, 4] we consider feature constraints as predicate logic formulae that are interpreted in the structure of feature trees. A feature tree is a possibly infinite tree with unordered labe... |

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Citation Context ...ability, entailment, complexity. 1 Introduction Feature constraints have been used for describing records in constraint programming [2, 24, 23] and record like structures in computational linguistics =-=[13, 12, 20, 18, 19]-=-. Following [3, 5, 4] we consider feature constraints as predicate logic formulae that are interpreted in the structure of feature trees. A feature tree is a possibly infinite tree with unordered labe... |

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Citation Context ...ords: feature constraints, tree orderings, weak subsumption, satisfiability, entailment, complexity. 1 Introduction Feature constraints have been used for describing records in constraint programming =-=[2, 24, 23]-=- and record like structures in computational linguistics [13, 12, 20, 18, 19]. Following [3, 5, 4] we consider feature constraints as predicate logic formulae that are interpreted in the structure of ... |

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Citation Context ...since a formula ϕ��� ϕ is valid if and only if the formula ϕ� ��� ϕ is unsatisfiable. To establish our result, we prove that FT� has the fundamental independence property (similar to its relatives RT =-=[6]-=-, FT [3], and CFT [24]). We reduce the satisfiability problem of Dörre’s weak-subsumption constraints [7] over feature algebras linearly to the one in FT� . Thereby, our algorithm improves on the best... |

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Citation Context ... 1 Introduction Feature constraints have been used for describing records in constraint programming [2, 24, 23] and record like structures in computational linguistics [13, 12, 20, 18, 19]. Following =-=[3, 5, 4]-=- we consider feature constraints as predicate logic formulae that are interpreted in the structure of feature trees. A feature tree is a possibly infinite tree with unordered labeled edges and with po... |

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Citation Context ...formal definition later). Apart from the mentioned tree constraint systems RT, FT , CFT [6, 1, 24, 3], constraint systems with the independence property include linear equations over the real numbers =-=[14]-=-, or infinite boolean algebras with positive constraints [10]. 3 Syntax and Semantics of FT£ The constraint system FT� is defined by a set of constraints together with an interpretation over feature t... |

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Citation Context ...umption is an ordering on the domain of feature algebras. Subsumption constraints have been considered in the context of unification-based grammars to model coordination phenomena in natural language =-=[9, 7, 21]-=-. There, one wants to express that two feature structures representing different parts of speech share common properties. For example, the analysis of “programming” and “linguistics” in the phrase Fea... |

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Citation Context ... 1 Introduction Feature constraints have been used for describing records in constraint programming [2, 24, 23] and record like structures in computational linguistics [13, 12, 20, 18, 19]. Following =-=[3, 5, 4]-=- we consider feature constraints as predicate logic formulae that are interpreted in the structure of feature trees. A feature tree is a possibly infinite tree with unordered labeled edges and with po... |

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Citation Context ... 1 Introduction Feature constraints have been used for describing records in constraint programming [2, 24, 23] and record like structures in computational linguistics [13, 12, 20, 18, 19]. Following =-=[3, 5, 4]-=- we consider feature constraints as predicate logic formulae that are interpreted in the structure of feature trees. A feature tree is a possibly infinite tree with unordered labeled edges and with po... |

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Citation Context ...raint systems RT, FT , CFT [6, 1, 24, 3], constraint systems with the independence property include linear equations over the real numbers [14], or infinite boolean algebras with positive constraints =-=[10]-=-. 3 Syntax and Semantics of FT£ The constraint system FT� is defined by a set of constraints together with an interpretation over feature trees. We assume an infinite set of variables ranged over by x... |

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Citation Context ...ion constraints and reduces their satisfiability problem to the one of FT� constraints. Section 7 shows that FT� is strictly more expressive than FT. 2 Related Work Ines Constraints. In previous work =-=[17]-=-, we have introduced the constraint system INES of inclusion constraints over non-empty sets of trees and a cubic satisfiability test. The satisfiability test for FT� is inspired by and subsumes the o... |

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Citation Context ...ated conjuncts are independent from each other, or: its constraints cannot express disjunctions (we will give a formal definition later). Apart from the mentioned tree constraint systems RT, FT , CFT =-=[6, 1, 24, 3]-=-, constraint systems with the independence property include linear equations over the real numbers [14], or infinite boolean algebras with positive constraints [10]. 3 Syntax and Semantics of FT£ The ... |

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Citation Context ...sult, we prove that FT� has the fundamental independence property (similar to its relatives RT [6], FT [3], and CFT [24]). We reduce the satisfiability problem of Dörre’s weak-subsumption constraints =-=[7]-=- over feature algebras linearly to the one in FT� . Thereby, our algorithm improves on the best known satisfiability test for weak subsumption constraints which uses finite automata techniques and has... |

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