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A Descriptive Approach to LanguageTheoretic Complexity
, 1996
"... Contents 1 Language Complexity in Generative Grammar 3 Part I The Descriptive Complexity of Strongly ContextFree Languages 11 2 Introduction to Part I 13 3 Trees as Elementary Structures 15 4 L 2 K;P and SnS 25 5 Definability and NonDefinability in L 2 K;P 35 6 Conclusion of Part I 57 DRAFT ..."
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Cited by 59 (3 self)
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Contents 1 Language Complexity in Generative Grammar 3 Part I The Descriptive Complexity of Strongly ContextFree Languages 11 2 Introduction to Part I 13 3 Trees as Elementary Structures 15 4 L 2 K;P and SnS 25 5 Definability and NonDefinability in L 2 K;P 35 6 Conclusion of Part I 57 DRAFT 2 / Contents Part II The Generative Capacity of GB Theories 59 7 Introduction to Part II 61 8 The Fundamental Structures of GB Theories 69 9 GB and Nondefinability in L 2 K;P 79 10 Formalizing XBar Theory 93 11 The Lexicon, Subcategorization, Thetatheory, and Case Theory 111 12 Binding and Control 119 13 Chains 131 14 Reconstruction 157 15 Limitations of the Interpretation 173 16 Conclusion of Part II 179 A Index of Definitions 183 Bibliography DRAFT 1<
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 41 (17 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.
Talking about Trees and TruthConditions
 Journal of Logic, Language and Information
, 2001
"... We present Logical Description Grammar (LDG), a model of grammar and the syntaxsemantics interface based on descriptions in elementary logic. A description may simultaneously describe the syntactic structure and the semantics of a natural language expression, i.e., the describing logic talks about ..."
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Cited by 28 (5 self)
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We present Logical Description Grammar (LDG), a model of grammar and the syntaxsemantics interface based on descriptions in elementary logic. A description may simultaneously describe the syntactic structure and the semantics of a natural language expression, i.e., the describing logic talks about the trees and about the truthconditions of the language described. Logical Description Grammars o er a natural way of dealing with underspeci cation in natural language syntax and semantics. If a logical description (up to isomorphism) has exactly one tree plus truthconditions as a model, it completely speci es that grammatical object. More common is the situation, corresponding to underspeci cation, in which there is more than one model. A situation in which there are no models corresponds to an ungrammatical input.
Axiomatizing the logical core of XPath 2.0
 In Th. Schwentick and D. Suciu, editors, Proceedings ICDT 2007
, 2007
"... The first aim of this paper is to present the logical core of XPath 2.0: a logically clean, decidable fragment, which includes most navigational features of XPath 2.0 (complex counting conditions and data joins are not supported, as they lead to undecidability). The second aim is to provide a list o ..."
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Cited by 26 (7 self)
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The first aim of this paper is to present the logical core of XPath 2.0: a logically clean, decidable fragment, which includes most navigational features of XPath 2.0 (complex counting conditions and data joins are not supported, as they lead to undecidability). The second aim is to provide a list of equations completely axiomatizing query equivalence in this language (i.e., all other query equivalences can be derived from these).
Dominance Constraints with Set Operators
 In Proceedings of the First International Conference on Computational Logic (CL2000), LNCS
, 2000
"... Dominance constraints are widely used in computational linguistics as a language for talking and reasoning about trees. In this paper, we extend dominance constraints by admitting set operators. We present a solver for dominance constraints with set operators, which is based on propagation and d ..."
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Cited by 23 (16 self)
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Dominance constraints are widely used in computational linguistics as a language for talking and reasoning about trees. In this paper, we extend dominance constraints by admitting set operators. We present a solver for dominance constraints with set operators, which is based on propagation and distribution rules, and prove its soundness and completeness.
A New Algorithm for Normal Dominance Constraints
 In Proc. SODA
, 2003
"... this paper, we propose a novel graph algorithm relying on graph connectivity, and inspired by [3]. It can enumerate all solved forms of a normal dominance constraint 2 ) per solved form, and thereby improves on the best previously known algorithm in e#ciency. # Humboldt Universitat zu Berlin, Germa ..."
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Cited by 17 (5 self)
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this paper, we propose a novel graph algorithm relying on graph connectivity, and inspired by [3]. It can enumerate all solved forms of a normal dominance constraint 2 ) per solved form, and thereby improves on the best previously known algorithm in e#ciency. # Humboldt Universitat zu Berlin, Germany + LORIA, Nancy, France # INRIA team Mostrare, Universite de Lille, France Universitat des Saarlandes, Germany Subquadratic running time can be achieved employing decremental graph biconnectivity algorithms
Combining tree partitioning, precedence, incomparability, and degree constraints, with an application to phylogenetic and orderedpath problems
, 2006
"... Abstract. The tree and path constraints, for digraph partitioning by vertexdisjoint trees and paths respectively, are unified within a single global constraint, including a uniform treatment of a variety of useful side constraints, such as precedence, incomparability, and degree constraints. The app ..."
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Cited by 16 (5 self)
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Abstract. The tree and path constraints, for digraph partitioning by vertexdisjoint trees and paths respectively, are unified within a single global constraint, including a uniform treatment of a variety of useful side constraints, such as precedence, incomparability, and degree constraints. The approach provides a sharp improvement over an existing path constraint, but can also efficiently handle tree problems, such as the phylogenetic supertree construction problem. The key point of the filtering is to take partially into account the strong interactions between the tree partitioning problem and all the side constraints. 1
Language, Lambdas, and Logic
 Resource Sensitivity in Binding and Anaphora
, 2003
"... Categorial Grammars'. Section 4 then continues with a closer look at possible ways to set up a particular Lambda Grammar, lling in some design choices. In particular we will opt for a three dimensional grammar there; one component will deal with dominance and precedence, one with semantics, an ..."
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Cited by 15 (1 self)
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Categorial Grammars'. Section 4 then continues with a closer look at possible ways to set up a particular Lambda Grammar, lling in some design choices. In particular we will opt for a three dimensional grammar there; one component will deal with dominance and precedence, one with semantics, and one with syntactic features. These choices bring us in close contact with the traditional architecture of LexicalFunctional Grammar (LFG, (Kaplan and Bresnan 1982), for further connections with LFG see (Oehrle 1999) and (Muskens 2001a), which is based upon the present system) and indeed the LFG architecture inspires our answer to question 4 above. Section 4 also works out the logics of the three grammatical components in some detail and thus illustrates one possible set of answers to question 3. For the semantic component we choose a standard type logic with possible worlds; for the feature component a type logic over the rstorder theory of features ((Johnson 1991)); and the multimodal approach to grammar that is found in most modern versions of the Lambek Calculus (see (Moortgat 1997) and references therein) will serve as a basis of the component dealing with dominance and precedence. The multimodal approach is thus moved from the general level of combing signs to one of the special dimensions of the grammar, another illustration of the modularity of the setup. The chapter ends with a short conclusion.
Underspecified Semantics
, 1999
"... Ambiguities in natural language can multiply so fast that no person or machine can be expected to process a text of even moderate length by enumerating all possible disambiguations. A sentence containing $n$ scope bearing elements which are freely permutable will have $n!$ readings, if there are no ..."
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Cited by 14 (8 self)
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Ambiguities in natural language can multiply so fast that no person or machine can be expected to process a text of even moderate length by enumerating all possible disambiguations. A sentence containing $n$ scope bearing elements which are freely permutable will have $n!$ readings, if there are no other, say lexical or syntactic, sources of ambiguity. A series of $m$ such sentences would lead to $(n!)^m$ possibilities. Some alternative scopings may boil down to the same reading. The relative order in which we scope two existentially quantified noun phrases, for example, will not matter if no other material intervenes. But all in all the growth of possibilities will be so fast that generating readings first and testing their acceptability afterwards will not be feasible.
Primitive CCommand
 Hopkins University, Baltimore and University of Delaware
, 1999
"... Work in syntactic theory has almost universally assumed that phrase structure is characterized in terms of the abstract structural relations of dominance and precedence. In this paper, we suggest instead that hierarchical structure is determined by a primitive relation of ccommand. This proposal ..."
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Cited by 14 (6 self)
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Work in syntactic theory has almost universally assumed that phrase structure is characterized in terms of the abstract structural relations of dominance and precedence. In this paper, we suggest instead that hierarchical structure is determined by a primitive relation of ccommand. This proposal has the consequence that the range of possible phrase structures is substantially restricted in a linguistically natural way, obviating the need for certain previously stipulated restrictions. Furthermore, by understanding structure in terms of primitive ccommand, we arrive at a natural understanding of the structural and derivational differences between substitution and adjunction, without resort to the machinery of segments and categories. keywords: phrase structure, ccommand, dominance, branching, adjunction, derivations Any descriptively adequate grammatical theory must precisely specify the wellformed representations for the sentences of all possible human languages. Part of th...