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26
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 67 (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 43 (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 Equality Upto Constraints over Finite Trees, Context Unification, and OneStep Rewriting
"... We introduce equality upto constraints over finite trees and investigate their expressiveness. Equality upto constraints subsume equality constraints, subtree constraints, and onestep rewriting constraints. ..."
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Cited by 27 (7 self)
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We introduce equality upto constraints over finite trees and investigate their expressiveness. Equality upto constraints subsume equality constraints, subtree constraints, and onestep rewriting constraints.
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 26 (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 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 17 (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.
Wellnested context unification
 In CADE 2005, LNCS 3632
"... Abstract. Context unification (CU) is the open problem of solving context equations for trees. We distinguish a new decidable variant of CU– wellnested CU – and present a new unification algorithm that solves wellnested context equations in nondeterministic polynomial time. We show that minimal w ..."
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Cited by 14 (8 self)
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Abstract. Context unification (CU) is the open problem of solving context equations for trees. We distinguish a new decidable variant of CU– wellnested CU – and present a new unification algorithm that solves wellnested context equations in nondeterministic polynomial time. We show that minimal wellnested solutions of context equations can be composed from the material present in the equation (see Theorem 1). This property is wishful when modeling natural language ellipsis in CU. 1
Processing underspecified semantic representations in the constraint language for lambda structures
 JOURNAL OF LANGUAGE AND COMPUTATION
, 2001
"... The constraint language for lambda structures (CLLS) is an expressive language of tree descriptions which combines dominance constraints with powerful parallelism and binding constraints. CLLS was introduced as a uniform framework for defining underspecified semantics representations of natural lang ..."
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Cited by 10 (9 self)
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The constraint language for lambda structures (CLLS) is an expressive language of tree descriptions which combines dominance constraints with powerful parallelism and binding constraints. CLLS was introduced as a uniform framework for defining underspecified semantics representations of natural language sentences, covering scope, ellipsis, and anaphora. This article presents saturationbased algorithms for processing the complete language of CLLS. It also gives an overview of previous results on questions of processing and complexity.
Context matching for compressed terms
 In LICS 2008
, 2008
"... This paper is an investigation of the matching problem for term equations s = t where s contains context variables, and both terms s and t are given using some kind of compressed representation. In this setting, term representation with dags, but also with the more general formalism of singleton t ..."
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Cited by 8 (6 self)
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This paper is an investigation of the matching problem for term equations s = t where s contains context variables, and both terms s and t are given using some kind of compressed representation. In this setting, term representation with dags, but also with the more general formalism of singleton tree grammars, are considered. The main result is a polynomial time algorithm for context matching with dags, when the number of different context variables is fixed for the problem. NPcompleteness is obtained when the terms are represented using singleton tree grammars. The special cases of firstorder matching and also unification with STGs are shown to be decidable in PTIME. 1
Context unification and traversal equations
 In: Proc. of the 12th International Conference on Rewriting Techniques and Applications (RTA’01
, 2001
"... Abstract. Context unification was originally defined by H. Comon in ICALP’92, as the problem of finding a unifier for a set of equations containing firstorder variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are secon ..."
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Cited by 8 (7 self)
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Abstract. Context unification was originally defined by H. Comon in ICALP’92, as the problem of finding a unifier for a set of equations containing firstorder variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are secondorder variables that are restricted to be instantiated by linear terms (a linear term is a λexpression λx1 ···λxn.t where every xi occurs exactly once in t). In this paper, we prove that, if the so called rankbound conjecture is true, then the context unification problem is decidable. This is done reducing context unification to solvability of traversal equations (a kind of word unification modulo certain permutations) and then, reducing traversal equations to word equations with regular constraints. 1