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An Efficient Graph Algorithm for Dominance Constraints
 JOURNAL OF ALGORITHMS
, 2003
"... Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NPcomplete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiablity in dete ..."
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Cited by 44 (18 self)
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Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NPcomplete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiablity in deterministic polynomial time. Previously, no polynomial time algorithm was known.
Bridging the Gap Between Underspecification Formalisms: Hole Semantics as Dominance Constraints
 In Proceedings of the 11th EACL
, 2003
"... We define a backandforth translation between Hole Semantics and dominance constraints, two formalisms used in underspecified semantics. There are fundamental differences between the two, but we show that they disappear on practically useful descriptions. Our encoding bridges a gap between t ..."
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Cited by 22 (9 self)
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We define a backandforth translation between Hole Semantics and dominance constraints, two formalisms used in underspecified semantics. There are fundamental differences between the two, but we show that they disappear on practically useful descriptions. Our encoding bridges a gap between two underspecification formalisms, and speeds up the processing of Hole Semantics.
Pure Dominance Constraints
, 2002
"... We present an efficient algorithm that checks the satisfiability of pure dominance constraints, which is a tree description language contained in several constraint languages studied in computational linguistics. Pure dominance constraints partially describe unlabeled rooted trees. For arbitrary pai ..."
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Cited by 13 (10 self)
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We present an efficient algorithm that checks the satisfiability of pure dominance constraints, which is a tree description language contained in several constraint languages studied in computational linguistics. Pure dominance constraints partially describe unlabeled rooted trees. For arbitrary pairs of nodes they specify sets of admissible relative positions in a tree. The task is to find a tree structure satisfying these constraints. Our algorithm constructs such a solution in time O(m^2) where m is the number of constraints. This solves an essential part of an open problem posed by Cornell.
WellNested Parallelism Constraints for Ellipsis Resolution
 IN 11TH CONFERENCE OF THE EUROPEAN CHAPTER OF THE ASSOCIATION OF COMPUTATIONAL LINGUISTICS
, 2003
"... The Constraint Language for Lambda Structures (CLLS) is an expressive tree description language. It provides a uniform framework for underspecified semantics, covering scope, ellipsis, and anaphora. Efficient algorithms exist for the sublanguage that models scope. But so far no terminating al ..."
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Cited by 5 (3 self)
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The Constraint Language for Lambda Structures (CLLS) is an expressive tree description language. It provides a uniform framework for underspecified semantics, covering scope, ellipsis, and anaphora. Efficient algorithms exist for the sublanguage that models scope. But so far no terminating algorithm exists for sublanguages that model ellipsis. We introduce wellnested parallelism constraints and show that they solve this problem.
Underspecified beta reduction
 In: Proceedings of the 39th ACL
, 2001
"... www.ps.unisb.de/˜{bodirskyerkniehren} For ambiguous sentences, traditional semantics construction produces large numbers of higherorder formulas, which must then be βreduced individually. Underspecified versions can produce compact descriptions of all readings, but it is not known how to perfor ..."
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Cited by 5 (3 self)
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www.ps.unisb.de/˜{bodirskyerkniehren} For ambiguous sentences, traditional semantics construction produces large numbers of higherorder formulas, which must then be βreduced individually. Underspecified versions can produce compact descriptions of all readings, but it is not known how to perform βreduction on these descriptions. We show how to do this using βreduction constraints in the constraint language for λstructures (CLLS).
Describing Lambda Terms in Context Unification
 in &quot;5th International Conference on Logical Aspects in Computational Linguistics&quot;, LNAI, vol. 3492, SV
, 2005
"... The constraint language for lambda structures (CLLS) is a description language for lambda terms. CLLS provides parallelism constraints to talk about the tree structure of lambda terms, and lambda binding constraints to specify variable binding. Parallelism constraints alone have the same express ..."
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Cited by 4 (1 self)
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The constraint language for lambda structures (CLLS) is a description language for lambda terms. CLLS provides parallelism constraints to talk about the tree structure of lambda terms, and lambda binding constraints to specify variable binding. Parallelism constraints alone have the same expressiveness as context unification. In this paper, we show that lambda binding constraints can also be expressed in context unification when permitting tree regular constraints.
Parallelism and Tree Regular Constraints
"... Abstract. Parallelism constraints are logical descriptions of trees. Parallelism constraints subsume dominance constraints and are equal in expressive power to context unification. Parallelism constraints belong to the constraint language for lambda structures (CLLS) which serves for modeling natura ..."
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Abstract. Parallelism constraints are logical descriptions of trees. Parallelism constraints subsume dominance constraints and are equal in expressive power to context unification. Parallelism constraints belong to the constraint language for lambda structures (CLLS) which serves for modeling natural language semantics. In this paper, we investigate the extension of parallelism constraints by tree regular constraints. This canonical extension is subsumed by the monadic secondorder logic over parallelism constraints. We analyze the precise expressiveness of this extension on basis of a new relationship between tree automata and logic. Our result is relevant for classifying different extensions of parallelism constraints, as in CLLS. Finally, we prove that parallelism constraints and context unification remain equivalent when extended with tree regular constraints.
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"... Abstract. This paper presents the Constraint Language for Lambda Structures (CLLS), a firstorder language for semantic underspecification that conservatively extends dominance constraints. It is interpreted over lambda structures, treelike structures that encode λterms. Based on CLLS, we present ..."
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Abstract. This paper presents the Constraint Language for Lambda Structures (CLLS), a firstorder language for semantic underspecification that conservatively extends dominance constraints. It is interpreted over lambda structures, treelike structures that encode λterms. Based on CLLS, we present an underspecified, uniform analysis of scope, ellipsis, anaphora, and their interactions. CLLS solves a variable capturing problem that is omnipresent in scope underspecification and can be processed efficiently.
VP Ellipsis by Tree Surgery  Extended Version
, 2001
"... We present jigsaw parallelism constraints, a flexible formal tool for replacing parts of trees with other trees. Jigsaw constraints extend the Constraint Language for Lambda Structures, a language used in underspecified semantics to declaratively describe scope, ellipsis, and their interaction, ..."
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We present jigsaw parallelism constraints, a flexible formal tool for replacing parts of trees with other trees. Jigsaw constraints extend the Constraint Language for Lambda Structures, a language used in underspecified semantics to declaratively describe scope, ellipsis, and their interaction, and can be used to improve the coverage of ellipses represented by CLLS.
On Lambda Binding Constraints and Context Unification
"... Abstract. Lambda binding and parallelism constraints are the main ingredients of the constraint language for lambda structures. Parallelism constraints alone are known to have the same expressive power as the language of context unification. Lambda binding constraints however were never investigated ..."
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Abstract. Lambda binding and parallelism constraints are the main ingredients of the constraint language for lambda structures. Parallelism constraints alone are known to have the same expressive power as the language of context unification. Lambda binding constraints however were never investigated in that framework. We show that lambda binding plus parallelism constraints can be expressed in context unification with tree regular constraints. 1