#### DMCA

## Describing Lambda Terms in Context Unification (2005)

### Cached

### Download Links

- [www.ps.uni-sb.de]
- [hal.inria.fr]
- [hal.univ-lille3.fr]
- [hal.inria.fr]
- DBLP

### Other Repositories/Bibliography

Venue: | in "5th International Conference on Logical Aspects in Computational Linguistics", LNAI, vol. 3492, SV |

Citations: | 4 - 1 self |

### Citations

202 |
Generalized finite automata theory with an application to a decision problem of second-order logic.
- THATCHER, WRIGHT
- 1968
(Show Context)
Citation Context ...U with tree regular constraints. This result is far from obvious. Our encoding requires several steps, one of which exploits an extension of the classical relationship between logic and tree automata =-=[17, 23]-=-. Another step relies on an important property of lambda binding constraints that we exhibit for the first time. We proceed as follows: we start with an example of parallel lambda binding (Sec. 2), re... |

120 |
D-Theory: Talking about talking about trees.
- Marcus, Hindle, et al.
- 1983
(Show Context)
Citation Context ...tion to CU with tree regular constraints (Sec. 9). Finally, we discuss some applications and limitations (Sec. 10). 2 Example and Application Parallelism constraints [8] subsume dominance constraints =-=[1, 2, 15]-=- which have multiple applications in computational linguistics: in syntax, semantics, and discourse (see e.g. [5, 24]). The prime application of CLLS, however, is to model under-specification in natur... |

97 | The Constraint Language for Lambda Structures. Logic, Language, and Information,
- Egg, Koller, et al.
- 2001
(Show Context)
Citation Context ...tion, equational logic and term rewriting, lambda and combinatory calculi,... 1 Introduction The constraint language for lambda structures (CLLS) is a first-order language for describing lambda terms =-=[6, 7]-=-. CLLS provides parallelism constraints [8] to talk about the tree structure of lambda terms, and lambda binding constraints to specify variable binding. In particular, CLLS models the interaction of ... |

82 | Using description of trees in a tree adjoining grammar
- Vijay-Shanker
- 1992
(Show Context)
Citation Context ...ample and Application Parallelism constraints [8] subsume dominance constraints [1, 2, 15] which have multiple applications in computational linguistics: in syntax, semantics, and discourse (see e.g. =-=[5, 24]-=-). The prime application of CLLS, however, is to model under-specification in natural language semantics [6, 7]. Consider for instance the sentence: John saw a taxi and so did Bill. This elliptic sent... |

70 | Radical underspecification.
- Pinkal
- 1996
(Show Context)
Citation Context ...inding cannot be expressed in LSOU or CU in any naive sense. In fact, this constitutes a serious problem to LSOU or other kinds of higher-order unification approaches to deal with ellipsis resolution =-=[18, 22]-=-. One might hope for instance, to describe the first reading above through the following lambda term: exists taxi #t.(and (C john) (C bill)) where C john = see john t The problem is that every unifier... |

68 | Completion of rewrite systems with membership constraints, to appear in
- Comon
- 1993
(Show Context)
Citation Context ... terms correctly. Parallelism constraints of CLLS alone have the same expressive power as equations of context unification (CU) [16], i.e. equations interpreted over the algebra of trees and contexts =-=[4]-=-. CU is closely related to linear second-order unifications(LSOU) [10] which restricts second-order unification to unifiers mapping to linear lambda-terms. This relationship can be made precise when a... |

53 | A First-Order Axiomatization of the Theory of Finite Trees
- Backofen, Rogers, et al.
- 1995
(Show Context)
Citation Context ...tion to CU with tree regular constraints (Sec. 9). Finally, we discuss some applications and limitations (Sec. 10). 2 Example and Application Parallelism constraints [8] subsume dominance constraints =-=[1, 2, 15]-=- which have multiple applications in computational linguistics: in syntax, semantics, and discourse (see e.g. [5, 24]). The prime application of CLLS, however, is to model under-specification in natur... |

41 | An efficient graph algorithm for dominance constraints.
- Althaus, Duchier, et al.
- 2003
(Show Context)
Citation Context ...tion to CU with tree regular constraints (Sec. 9). Finally, we discuss some applications and limitations (Sec. 10). 2 Example and Application Parallelism constraints [8] subsume dominance constraints =-=[1, 2, 15]-=- which have multiple applications in computational linguistics: in syntax, semantics, and discourse (see e.g. [5, 24]). The prime application of CLLS, however, is to model under-specification in natur... |

36 | Linear second-order unification,
- Levy
- 1996
(Show Context)
Citation Context ... expressive power as equations of context unification (CU) [16], i.e. equations interpreted over the algebra of trees and contexts [4]. CU is closely related to linear second-order unifications(LSOU) =-=[10]-=- which restricts second-order unification to unifiers mapping to linear lambda-terms. This relationship can be made precise when allowing for additional tree regular constraints [13] which help to avo... |

28 | Solvability of context equations with two context variables is decidable - Schulz - 1999 |

25 | Bridging the gap between underspecification formalisms: Minimal recursion semantics as dominance constraints.
- Niehren, Thater
- 2003
(Show Context)
Citation Context ...correctly. CLLS supports parallelism constraints to model ellipsis in natural language. These subsume dominance constraints [13, 23, 1, 4], an excellent modeling language for scope underspecification =-=[15]-=-. CLLS features lambda binding constraints in order to analyze the interactions of scope and ellipsis, i.e., parallel lambda binding. Further ingredients of CLLS are anaphoric binding constraints, gro... |

15 | Interaction of scope and ellipsis
- Shieber, Pereira, et al.
- 1999
(Show Context)
Citation Context ...inding cannot be expressed in LSOU or CU in any naive sense. In fact, this constitutes a serious problem to LSOU or other kinds of higher-order unification approaches to deal with ellipsis resolution =-=[18, 22]-=-. One might hope for instance, to describe the first reading above through the following lambda term: exists taxi #t.(and (C john) (C bill)) where C john = see john t The problem is that every unifier... |

13 | Dominance constraints in context unification
- Niehren, Koller
- 1998
(Show Context)
Citation Context ...LLS models the interaction of parallelism and variable binding in lambda terms correctly. Parallelism constraints of CLLS alone have the same expressive power as equations of context unification (CU) =-=[16]-=-, i.e. equations interpreted over the algebra of trees and contexts [4]. CU is closely related to linear second-order unifications(LSOU) [10] which restricts second-order unification to unifiers mappi... |

11 | Tree descriptions, constraints and incrementality
- Duchier, Gardent
- 2001
(Show Context)
Citation Context ...ample and Application Parallelism constraints [8] subsume dominance constraints [1, 2, 15] which have multiple applications in computational linguistics: in syntax, semantics, and discourse (see e.g. =-=[5, 24]-=-). The prime application of CLLS, however, is to model under-specification in natural language semantics [6, 7]. Consider for instance the sentence: John saw a taxi and so did Bill. This elliptic sent... |

10 | Processing underspecified semantic representations in the constraint language for lambda structures
- Erk, Koller, et al.
(Show Context)
Citation Context ...tion, equational logic and term rewriting, lambda and combinatory calculi,... 1 Introduction The constraint language for lambda structures (CLLS) is a first-order language for describing lambda terms =-=[6, 7]-=-. CLLS provides parallelism constraints [8] to talk about the tree structure of lambda terms, and lambda binding constraints to specify variable binding. In particular, CLLS models the interaction of ... |

10 | Parallelism constraints
- Erk, Niehren
- 2000
(Show Context)
Citation Context ...bda and combinatory calculi,... 1 Introduction The constraint language for lambda structures (CLLS) is a first-order language for describing lambda terms [6, 7]. CLLS provides parallelism constraints =-=[8]-=- to talk about the tree structure of lambda terms, and lambda binding constraints to specify variable binding. In particular, CLLS models the interaction of parallelism and variable binding in lambda ... |

10 | A decision algorithm for distributive unification - Schmidt-Schauß - 1998 |

8 | Beta reduction constraints
- Bodirsky, Erk, et al.
- 2001
(Show Context)
Citation Context .... . . [# n /. n ]).# . Proposition 13. A tree parallelism relation # 1 ## 2 holds between two segments of a tree # if and only if context # (# 1 ) = context # (# 2 ). 10 Limitations It is proposed in =-=[3]-=- to extend CLLS by group parallelism in order to deal with beta reduction constraints. The question is now whether group parallelism can be expressed in context unification with tree regular constrain... |

8 | Context unification and traversal equations
- Levy, Villaret
- 2001
(Show Context)
Citation Context ...he decidability of CU, LSOU, and CLLS-satisfiability with or without tree regular constraints are prominent open questions that are closely related. Decidability of CU was often conjectured (see e.g. =-=[14]-=-). This is because various restrictions [4, 10, 19--21] make CU decidable, while the analogous restrictions for second-order unification don't [11, 12]. An independent decidable fragment of CLLS was p... |

8 | A decision algorithm for distributive unification - Schmidt-Schau - 1998 |

8 | Decidability of bounded higher-order unification - Schmidt-Schauß, Schulz |

7 |
and Margus Veanes. On the undecidability of second-order unification
- Levy
(Show Context)
Citation Context .... Decidability of CU was often conjectured (see e.g. [14]). This is because various restrictions [4, 10, 19--21] make CU decidable, while the analogous restrictions for second-order unification don't =-=[11, 12]-=-. An independent decidable fragment of CLLS was presented recently [9]. In this paper, we contribute a more accurate comparison between CLLS and CU which does account for lambda binding constraints fo... |

5 | Well-nested parallelism constraints for ellipsis resolution
- Erk, Niehren
- 2003
(Show Context)
Citation Context ... various restrictions [4, 10, 19--21] make CU decidable, while the analogous restrictions for second-order unification don't [11, 12]. An independent decidable fragment of CLLS was presented recently =-=[9]-=-. In this paper, we contribute a more accurate comparison between CLLS and CU which does account for lambda binding constraints for the first time. The motivating question is whether it is possible to... |

5 |
and Mateu Villaret. Linear second-order unification and context unification with tree-regular constraints
- Levy
- 2000
(Show Context)
Citation Context ...nifications(LSOU) [10] which restricts second-order unification to unifiers mapping to linear lambda-terms. This relationship can be made precise when allowing for additional tree regular constraints =-=[13]-=- which help to avoid variable capture when translating lambda-terms from LSOU equations into CU equations. The decidability of CU, LSOU, and CLLS-satisfiability with or without tree regular constraint... |

5 | Underspecified beta reduction
- Bodirsky, Erk, et al.
- 2001
(Show Context)
Citation Context ...order to analyze the interactions of scope and ellipsis, i.e., parallel lambda binding. Further ingredients of CLLS are anaphoric binding constraints, group parallelism and beta reduction constraints =-=[2]-=-. Parallelism constraints of CLLS alone have the same expressive power as the context equations in context unification (CU) [14, 3]. CU is a variant of linear second-order unification (LSOU) [9] which... |

3 |
and Margus Veanes. On unification problems in restricted second-order languages
- Levy
- 1998
(Show Context)
Citation Context .... Decidability of CU was often conjectured (see e.g. [14]). This is because various restrictions [4, 10, 19--21] make CU decidable, while the analogous restrictions for second-order unification don't =-=[11, 12]-=-. An independent decidable fragment of CLLS was presented recently [9]. In this paper, we contribute a more accurate comparison between CLLS and CU which does account for lambda binding constraints fo... |

1 |
Niehren and Mateu Villaret. Parallelism and tree regular constraints
- Joachim
- 2002
(Show Context)
Citation Context ...U with tree regular constraints. This result is far from obvious. Our encoding requires several steps, one of which exploits an extension of the classical relationship between logic and tree automata =-=[17, 23]-=-. Another step relies on an important property of lambda binding constraints that we exhibit for the first time. We proceed as follows: we start with an example of parallel lambda binding (Sec. 2), re... |

1 | Decidability of bounded higherorder unification - Schmidt-Schau, Schulz - 2002 |