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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<
Dominance Constraints: Algorithms and Complexity
 IN PROCEEDINGS OF THE THIRD CONFERENCE ON LOGICAL ASPECTS OF COMPUTATIONAL LINGUISTICS
, 1998
"... Dominance constraints for finite tree structures are widely used in several areas of computational linguistics including syntax, semantics, and discourse. In this paper, we investigate algorithmic and complexity questions for dominance constraints and their firstorder theory. We present two NP algo ..."
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Cited by 40 (21 self)
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Dominance constraints for finite tree structures are widely used in several areas of computational linguistics including syntax, semantics, and discourse. In this paper, we investigate algorithmic and complexity questions for dominance constraints and their firstorder theory. We present two NP algorithms for solving dominance constraints, which have been implemented in the concurrent constraint programming language Oz. The main result of this paper is that the satisfiability problem of dominance constraints is NPcomplete. Despite this intractability result, the more sophisticated of our algorithms performs well in an application to scope underspecification. We also show that the existential fragment of the firstorder theory of dominance constraints is NPcomplete and that the full firstorder theory has nonelementary complexity.
On Determining The Consistency Of Partial Descriptions Of Trees
, 1994
"... We examine the consistency problem for descriptions of trees based on remote dominance, and present a consistencychecking algorithm which is polynomial in the number of nodes in the description, despite disjunctions inherent in the theory of trees. The resulting algorithm allows for descriptions ..."
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Cited by 29 (1 self)
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We examine the consistency problem for descriptions of trees based on remote dominance, and present a consistencychecking algorithm which is polynomial in the number of nodes in the description, despite disjunctions inherent in the theory of trees. The resulting algorithm allows for descriptions which go beyond sets of atomic formulas to allow certain types of disjunction and negation.
Treelocal multicomponent tree adjoining grammars with shared nodes
 COMPUTATIONAL LINGUISTICS
, 2005
"... This article addresses the problem that the expressive power of treeadjoining grammars (TAGs) is too limited to deal with certain syntactic phenomena, in particular, with scrambling in freewordorder languages. The TAG variants proposed so far in order to account for scrambling are not entirely sat ..."
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Cited by 15 (6 self)
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This article addresses the problem that the expressive power of treeadjoining grammars (TAGs) is too limited to deal with certain syntactic phenomena, in particular, with scrambling in freewordorder languages. The TAG variants proposed so far in order to account for scrambling are not entirely satisfying. Therefore, the article introduces an alternative extension of TAG that is based on the notion of node sharing, socalled (restricted) treelocal multicomponent TAG with shared nodes (RSNMCTAG). The analysis of some German scrambling data is sketched in order to show that this TAG extension can deal with scrambling. Then it is shown that for RSNMCTAGs of a specific type, equivalent simple range concatenation grammars can be constructed. As a consequence, these RSNMCTAGs are mildly contextsensitive and in particular polynomially parsable. These specific RSNMCTAGs probably can deal not with all scrambling phenomena, but with an arbitrarily large subset.
A ModelTheoretic Framework for Theories of Syntax
, 1996
"... A natural next step in the evolution of constraintbased grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanismto express syntactic theories purely in terms of the properties of the class of structures they license. By focusing on th ..."
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Cited by 14 (2 self)
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A natural next step in the evolution of constraintbased grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanismto express syntactic theories purely in terms of the properties of the class of structures they license. By focusing on the structural properties of languages rather than on mechanisms for generating or checking structures that exhibit those properties, this modeltheoretic approach can offer simpler and significantly clearer expression of theories and can potentially provide a uniform formalization, allowing disparate theories to be compared on the basis of those properties. We discuss L,p, a monadic secondorder logical framework for such an approach to syn tax that has the distinctive virtue of being superficially expressivesupporting direct statement of most linguistically significant syntactic properties  but having welldefined strong generative capacity  languages are definable in L,p iff they are strongly contextfree. We draw examples from the realms of GPSG and GB.
"Grammarless" Phrase Structure Grammar
, 1997
"... We sketch an axiomatic reformalization of Generalized Phrase Structure Grammar (GPSG)a definition purely within the language of mathematical logic of the theory GPSG embodies. While this treatment raises a number of theoretical issues for GPSG, our focus is not the reformalization itself but rath ..."
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Cited by 12 (5 self)
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We sketch an axiomatic reformalization of Generalized Phrase Structure Grammar (GPSG)a definition purely within the language of mathematical logic of the theory GPSG embodies. While this treatment raises a number of theoretical issues for GPSG, our focus is not the reformalization itself but rather the method we employ. The modeltheoretic approach it exemplifies can be seen as a natural step in the evolution of constraintbased theories from their grammarbased antecedents. One goal of this paper is to introduce this approach to a broader audience and to demonstrate its application to an existing theory. As such, it joins a growing literature of similar studies. Prior studies, however, have had a number of weaknessesthey generally offer little in the way of concrete examples of the advantages the approach has to offer, they typically ignore significant portions of the theories they address, and, by fully abstracting away from the notion of grammar mechanism, they largely abandon...
Contrasting applications of logic in natural language syntactic description
 Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress
, 2005
"... Abstract. Formal syntax has hitherto worked mostly with theoretical frameworks that take grammars to be generative, in Emil Post’s sense: they provide recursive enumerations of sets. This work has its origins in Post’s formalization of proof theory. There is an alternative, with roots in the semanti ..."
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Cited by 12 (1 self)
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Abstract. Formal syntax has hitherto worked mostly with theoretical frameworks that take grammars to be generative, in Emil Post’s sense: they provide recursive enumerations of sets. This work has its origins in Post’s formalization of proof theory. There is an alternative, with roots in the semantic side of logic: modeltheoretic syntax (MTS). MTS takes grammars to be sets of statements of which (algebraically idealized) wellformed expressions are models. We clarify the difference between the two kinds of framework and review their separate histories, and then argue that the generative perspective has misled linguists concerning the properties of natural languages. We select two elementary facts about natural language phenomena for discussion: the gradient character of the property of being ungrammatical and the open nature of natural language lexicons. We claim that the MTS perspective on syntactic structure does much better on representing the facts in these two domains. We also examine the arguments linguists give for the infinitude of the class of all expressions in a natural language. These arguments turn out on examination to be either unsound or lacking in empirical content. We claim that infinitude is an unsupportable claim that is also unimportant. What is actually needed is a way of representing the structure of expressions in a natural language without assigning any importance to the notion of a unique set with definite cardinality that contains all and only the expressions in the language. MTS provides that.
Model Theoretic Syntax
 The Glot International State of the Article Book 1, Studies in Generative Grammar 48, Mouton de Gruyter
, 1998
"... this article appeared in Glot, the main issue agitating researchers in model theoretic syntax was the problem of the contextfree barrier. We have seen that the hierarchy of logics collapses, when applied to trees, at the border of the tree languages strongly generated by context free (string) gramm ..."
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Cited by 11 (1 self)
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this article appeared in Glot, the main issue agitating researchers in model theoretic syntax was the problem of the contextfree barrier. We have seen that the hierarchy of logics collapses, when applied to trees, at the border of the tree languages strongly generated by context free (string) grammars, in the sense that distinctions between the different tree logics reduce to apparently superficial distinctions in how much memory allocation is hidden in the logic. The problem which researchers set themselves was not just breaking the context free barrier but remaining decidable in the process. This is a very difficult problem, and it must be admitted right off that it is somewhat artificial in that there is no a priori reason to suppose that natural languages can be described in a decidable logic. The arguments on either side are something like the following. First, the rather slight increases in computational complexity required to get the "mildly context sensitive" languages do suggest that this might be possible. The hunch here would be that the qualities that characterize the mildly context sensitive languages (polynomial parsability, constant growth property) as being like the contextfree languages are going to turn out to be reflections of decidability. The problems must not be underestimated, however! It is well known that the monadic second order logic of trees is one of the most powerful decidable logics known. It seems unlikely that any primitive relations can be added to the repertoire of tree description primitives that we have already seen, without making the logic undecidable. Many attempts have been made within logic and all have failed. So it is equally tempting to conjecture that the contextfree boundary coincides in some deep sense with the bounda...
Representing Constraints with Automata
, 1997
"... In this paper we describe an approach to constraint based syntactic theories in terms of finite tree automata. The solutions to constraints expressed in weak monadic second order (MSO) logic are represented by tree automata recognizing the assignments which make the formulas true. We show tha ..."
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Cited by 8 (2 self)
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In this paper we describe an approach to constraint based syntactic theories in terms of finite tree automata. The solutions to constraints expressed in weak monadic second order (MSO) logic are represented by tree automata recognizing the assignments which make the formulas true. We show that this allows an efficient representation of knowledge about the content of constraints which can be used as a practical tool for grammatical theory verification.
On Reducing Principles to Rules
 In Patrick Blackburn and Maarten de Rijke, editors, Specifying Syntactic Structure. CSLI
, 1997
"... According to the research principles of the tradition established by Noam Chomsky, one should always try to get rid of construction specific rules. In Bare Phrase Structure he has carried this out to the extreme for the basic generative component now known as Xbarsyntax. Based on this example, we ..."
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Cited by 7 (4 self)
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According to the research principles of the tradition established by Noam Chomsky, one should always try to get rid of construction specific rules. In Bare Phrase Structure he has carried this out to the extreme for the basic generative component now known as Xbarsyntax. Based on this example, we will examine the dialectics between specific rules and conditions on rules or principles. We will show that there is a twoway reduction, one from rules to conditions on rules, and the other from conditions on rules to specific rules. As an effect of this reduction, a particular linguistic theory can be presented alternatively as a set of rules or as an axiomatic extension of the logical theory of all phrase structure trees—or in fact a suitable mixture of the two. Although this reduction is a purely formal one—and therefore less interesting for a linguist subscribing to the Principles and Parameters approach—it offers the possibility to draw on a large array of results both from logic and from ordinary formal language theory. 1