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28
The Constraint Language for Lambda Structures
, 2000
"... 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 terms. Based on CLLS, we present an underspe ..."
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Cited by 101 (33 self)
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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 terms. 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.
On Semantic Underspecification
, 1999
"... . 1 Another important source for the interest in underspecification is lexical semantics. Example (2) is a representative for a large field of ambiguity phenomena, which are conventionally classified as lexical ambiguities, but differ from trivial cases like the homonyms bank or pen in several imp ..."
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Cited by 69 (2 self)
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. 1 Another important source for the interest in underspecification is lexical semantics. Example (2) is a representative for a large field of ambiguity phenomena, which are conventionally classified as lexical ambiguities, but differ from trivial cases like the homonyms bank or pen in several important ways. 1 Earlier, but less influential research on underspecification was performed in the phliqa project at Philips Research Labs, where it seems that the concept of `metavariables' was actually discovered; see e.g. Bronnenberg et al. (1979); Landsbergen & Scha (1979); Bunt (1984; 1985). boekpinkal.tex; 27/08/1999; 13:09; p.1 33 H. Bunt and R. Muskens (eds.) Computing Meaning. Kluwer Academic Press, Dordrecht 1999, 3355.. 34 MANFRED PINKAL (2) John began the book Rather than locating the source of ambiguity of sentence (2) in the verb b
Constraints over lambdastructures in semantic underspecification
 In Proc. of COLING/ACL
, 1998
"... niehren0ps, unisb, de We introduce a firstorder language for semantic underspecification that we call Constraint Language for LambdaStructures (CLLS). A Astructure can be considered as a Aterm up to consistent renaming of bound variables (aequality); a constraint of CLLS is an underspecified ..."
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Cited by 42 (16 self)
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niehren0ps, unisb, de We introduce a firstorder language for semantic underspecification that we call Constraint Language for LambdaStructures (CLLS). A Astructure can be considered as a Aterm up to consistent renaming of bound variables (aequality); a constraint of CLLS is an underspecified description of a Astructure. CLLS solves a capturing problem omnipresent in underspecified scope representations. CLLS features constraints for dominance, lambda binding, parallelism, and anaphoric links. Based on CLLS we present a simple, integrated, amt underspecified treatment of scope, parallelism, and anaphora. 1
On the Undecidability of SecondOrder Unification
 INFORMATION AND COMPUTATION
, 2000
"... ... this paper, and it is the starting point for proving some novel results about the undecidability of secondorder unification presented in the rest of the paper. We prove that secondorder unification is undecidable in the following three cases: (1) each secondorder variable occurs at most t ..."
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Cited by 36 (16 self)
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... this paper, and it is the starting point for proving some novel results about the undecidability of secondorder unification presented in the rest of the paper. We prove that secondorder unification is undecidable in the following three cases: (1) each secondorder variable occurs at most twice and there are only two secondorder variables; (2) there is only one secondorder variable and it is unary; (3) the following conditions (i)#(iv) hold for some fixed integer n: (i) the arguments of all secondorder variables are ground terms of size <n, (ii) the arity of all secondorder variables is <n, (iii) the number of occurrences of secondorder variables is #5, (iv) there is either a single secondorder variable or there are two secondorder variables and no firstorder variables.
Solvability of context equations with two context variables is decidable
 THE JOURNAL OF SYMBOLIC COMPUTATION
, 1999
"... Context unification is a natural variant of second order unification that represents a generalization of word unification at the same time. While second order unification is wellknown to be undecidable and word unification is decidable it is currently open if solvability of context equations is deci ..."
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Cited by 29 (2 self)
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Context unification is a natural variant of second order unification that represents a generalization of word unification at the same time. While second order unification is wellknown to be undecidable and word unification is decidable it is currently open if solvability of context equations is decidable. We show that solvability of systems of context equations with two context variables is decidable. The context variables may have an arbitrary number of occurrences, and the equations may contain an arbitrary number of individual variables as well. The result holds under the assumption that the first order background signature is finite.
A Uniform Approach to Underspecification and Parallelism
 In Proceedings ACL'97
, 1997
"... We propose a unified flamework in which to treat semantic underspecification and parallelism phenomena in discourse. The framework employs a constraint language that can express equality and subtree relations between finite trees. In addition, our constraint language can express the equality upto r ..."
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Cited by 28 (9 self)
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We propose a unified flamework in which to treat semantic underspecification and parallelism phenomena in discourse. The framework employs a constraint language that can express equality and subtree relations between finite trees. In addition, our constraint language can express the equality upto relation over trees which captures parallelism between them. The constraints are solved by context unification. We demonstrate the use of our framework at the examples of quantifier scope, ellipsis, and their interaction. 1 I
A decision algorithm for stratified context unification
 FACHBEREICH INFORMATIK, J.W. GOETHEUNIVERSITAT
, 1999
"... Context unification is a variant of second order unification and also a generalization of string unification. Currently it is not known whether context unification is decidable. A specialization of context unification is stratified context unification. Recently, it turned out that stratified context ..."
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Cited by 20 (1 self)
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Context unification is a variant of second order unification and also a generalization of string unification. Currently it is not known whether context unification is decidable. A specialization of context unification is stratified context unification. Recently, it turned out that stratified context unification and onestep rewrite constraints are equivalent. This paper contains a description of a decision algorithm SCU for stratified context unification, which shows decidability of stratified context unification as well as of satisfiability of onestep rewrite constraints.
Dominance Constraints in Context Unification
, 1998
"... Tree descriptions based on dominance constraints are popular in several areas of computational linguistics including syntax, semantics, and discourse. Tree descriptions in the language of context unification have attracted some interest in unification and rewriting theory. Recently, dominance constr ..."
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Cited by 14 (10 self)
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Tree descriptions based on dominance constraints are popular in several areas of computational linguistics including syntax, semantics, and discourse. Tree descriptions in the language of context unification have attracted some interest in unification and rewriting theory. Recently, dominance constraints and context unification have both been used in different underspecified approaches to the semantics of scope, parallelism, and their interaction. This raises the question whether both description languages are related. In this paper, we show for a first time that dominance constraints can be expressed in context unification. We also prove that dominance constraints extended with parallelism constraints are equal in expressive power to context unification.
Linear SecondOrder Unification and Context Unification with TreeRegular Constraints
 Proc. of the 11th Int. Conference on Rewriting Techniques and Applications (RTA’2000), volume 1833 of LNCS
, 2000
"... Linear SecondOrder Unification and Context Unification are closely related problems. However, their equivalence was never formally proved. Context unification is a restriction of linear secondorder unification. Here we prove that linear secondorder unification can be reduced to context unificatio ..."
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Cited by 12 (3 self)
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Linear SecondOrder Unification and Context Unification are closely related problems. However, their equivalence was never formally proved. Context unification is a restriction of linear secondorder unification. Here we prove that linear secondorder unification can be reduced to context unification with treeregular constraints. Decidability of context unification is still an open question. We comment on the possibility that linear secondorder unification is decidable, if context unification is, and how to get rid of the treeregular constraints. This is done by reducing rankbound treeregular constraints to wordregular constraints.
Stratified context unification is npcomplete
 In Proc. of the 3rd International Joint Conference on Automated Reasoning, IJCAR’06
, 2006
"... Abstract. Context Unification is the problem to decide for a given set of secondorder equations E where all secondorder variables are unary, whether there exists a unifier, such that for every secondorder variable X, theabstractionλx.r instantiated for X has exactly one occurrence of the bound va ..."
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Cited by 11 (3 self)
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Abstract. Context Unification is the problem to decide for a given set of secondorder equations E where all secondorder variables are unary, whether there exists a unifier, such that for every secondorder variable X, theabstractionλx.r instantiated for X has exactly one occurrence of the bound variable x in r. Stratified Context Unification is a specialization where the nesting of secondorder variables in E is restricted. It is already known that Stratified Context Unification is decidable, NPhard, and in PSPACE, whereas the decidability and the complexity of Context Unification is unknown. We prove that Stratified Context Unification is in NP by proving that a sizeminimal solution can be represented in a singleton tree grammar of polynomial size, and then applying a generalization of Plandowski’s polynomial algorithm that compares compacted terms in polynomial time. This also demonstrates the high potential of singleton tree grammars for optimizing programs maintaining large terms. A corollary of our result is that solvability of rewrite constraints is NPcomplete. 1