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19
Semilinearity as a Syntactic Invariant
, 1996
"... . Mildly context sensitive grammar formalisms such as multicomponent TAGs and linear context free rewrite systems have been introduced to capture the full complexity of natural languages. We show that, in a formal sense, Old Georgian can be taken to provide an example of a nonsemilinear languag ..."
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Cited by 20 (8 self)
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. Mildly context sensitive grammar formalisms such as multicomponent TAGs and linear context free rewrite systems have been introduced to capture the full complexity of natural languages. We show that, in a formal sense, Old Georgian can be taken to provide an example of a nonsemilinear language. This implies that none of the aforementioned grammar formalisms is strong enough to generate this language. Introduction What we have in mind when we use the term syntactic invariant is, roughly speaking, a property, valid within some (formal) grammar theory, which remains "robust under slight modifications" of this theory. In the following we direct our particular attention to one such property: Semilinearity (of a language). Introducing the definition of semilinearity Parikh proved that any context free language (CFL) is semilinear (see e.g. Parikh 1966). It has been shown that there is a need to go beyond the class of all CFLs, if we want to define a formal language in terms of phr...
Connectionist sentence processing in perspective
 Cognitive Science
, 1999
"... The emphasis in the connectionist sentenceprocessing literature on distributed representation and emergence of grammar from such systems can easily obscure the often close relations between connectionist and symbolist systems. This paper argues that the Simple Recurrent Network (SRN) models propose ..."
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Cited by 15 (2 self)
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The emphasis in the connectionist sentenceprocessing literature on distributed representation and emergence of grammar from such systems can easily obscure the often close relations between connectionist and symbolist systems. This paper argues that the Simple Recurrent Network (SRN) models proposed by Jordan (1989) and Elman (1990) are more directly related to stochastic PartofSpeech (POS) Taggers than to parsers or grammars as such, while autoassociative memory models of the kind pioneered by Longuet–Higgins, Willshaw, Pollack and others may be useful for grammar induction from a networkbased conceptual structure as well as for structurebuilding. These observations suggest some interesting new directions for specifically connectionist sentence processing research, including more efficient representations for finite state machines, and acquisition devices based on a distinctively connectionist basis for grounded symbolist conceptual structure. I.
Chinese NumberNames, Tree Adjoining Languages, and Mild ContextSensitivity
 COMPUTATIONAL LINGUISTICS
, 1991
"... ... this paper that the numbername system of Chinese is generated neither by this formalism nor by any other equivalent or weaker ones, suggesting that such a task might require the use of the more powerful Indexed Grammar formalism. Given that our formal results apply only to a proper subset of Ch ..."
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Cited by 14 (0 self)
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... this paper that the numbername system of Chinese is generated neither by this formalism nor by any other equivalent or weaker ones, suggesting that such a task might require the use of the more powerful Indexed Grammar formalism. Given that our formal results apply only to a proper subset of Chinese, we extensively discuss the issue of whether they have any implications for the whole of that natural language. We conclude that our results bear directly either on the syntax of Chinese or on the interface between Chinese and the cognitive component responsible for arithmetic reasoning. Consequently, either Tree Adjoining Grammars, as currently defined, fail to generate the class of natural languages in a way that discriminates between linguistically warranted sublanguages, or formalisms with generative power equivalent to Tree Adjoining Grammar cannot serve as a basis for the interface between the human linguistic and mathematical faculties.
Syntactic Structures as Multidimensional Trees
"... We survey a sequence of results relating modeltheoretic and languagetheoretic
denability over an innite hierarchy of multidimensional treelike structures and explore
their applications to a corresponding range of theories of syntax. We discuss, in particular,
results for Government and Binding T ..."
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Cited by 14 (0 self)
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We survey a sequence of results relating modeltheoretic and languagetheoretic
denability over an innite hierarchy of multidimensional treelike structures and explore
their applications to a corresponding range of theories of syntax. We discuss, in particular,
results for Government and Binding Theory (GB), TreeAdjoining Grammar (TAG) and
Generalized PhraseStructure Grammar (GPSG) along with a generalized version of TAG
extending TAG in much the same way that GPSG extends CFLs. In addition, we look at a
hierarchy of language classes, Weir’s version of the Control Language Hierarchy, which is
characterized by denability in our hierarchy and speculate on possible linguistic signicance
of higher levels of these hierarchies.
"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...
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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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...
Efficient Parsing of WellNested Linear ContextFree Rewriting Systems
"... The use of wellnested linear contextfree rewriting systems has been empirically motivated for modeling of the syntax of languages with discontinuous constituents or relatively free word order. We present a chartbased parsing algorithm that asymptotically improves the known running time upper boun ..."
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Cited by 7 (2 self)
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The use of wellnested linear contextfree rewriting systems has been empirically motivated for modeling of the syntax of languages with discontinuous constituents or relatively free word order. We present a chartbased parsing algorithm that asymptotically improves the known running time upper bound for this class of rewriting systems. Our result is obtained through a linear space construction of a binary normal form for the grammar at hand. 1
Monadic SecondOrder Logic and Transitive Closure Logics over Trees
"... Model theoretic syntax is concerned with studying the descriptive complexity of grammar formalisms for natural languages by defining their derivation trees in suitable logical formalisms. The central tool for model theoretic syntax has been monadic secondorder logic (MSO). Much of the recent resear ..."
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Model theoretic syntax is concerned with studying the descriptive complexity of grammar formalisms for natural languages by defining their derivation trees in suitable logical formalisms. The central tool for model theoretic syntax has been monadic secondorder logic (MSO). Much of the recent research in this area has been concerned with finding more expressive logics to capture the derivation trees of grammar formalisms that generate noncontextfree languages. The motivation behind this search for more expressive logics is to describe formally certain mildly contextsensitive phenomena of natural languages. Several extensions to MSO have been proposed, most of which no longer define the derivation trees of grammar formalisms directly, while others introduce logically odd restrictions. We therefore propose to consider firstorder transitive closure logic. In this logic, derivation trees can be defined in a direct way. Our main result is that transitive closure logic, even deterministic transitive closure logic, is more expressive in defining classes of tree languages than MSO. (Deterministic) transitive closure logics are capable of defining nonregular tree languages that are of interest to linguistics.
What Does a Grammar Formalism Say About a Language?
, 1996
"... Over the last ten or fifteen years there has been a shift in generative linguistics away from formalisms based on a procedural interpretation of grammars towards constraintbased formalismsformalisms that define languages by specifying a set of constraints that characterize the set of wellformed s ..."
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Cited by 5 (1 self)
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Over the last ten or fifteen years there has been a shift in generative linguistics away from formalisms based on a procedural interpretation of grammars towards constraintbased formalismsformalisms that define languages by specifying a set of constraints that characterize the set of wellformed structures analyzing the strings in the language. A natural extension of this trend is to define this set of structures modeltheoretically  to define it as the set of mathematical structures that satisfy some set of logical axioms. This approach raises a number of questions about the nature of linguistic theories and the role of grammar formalisms in expressing them. We argue here that the crux of what theories of syntax have to say about language lies in the abstract properties of the sets of structures they license. This is the level that is most directly connected to the empirical basis of these theories and it is the level at which it is possible to make meaningful comparisons between the approaches. From this point of view, grammar formalisms (or formal frameworks) are primarily means of presenting these properties. Many of the apparent distinctions between formalisms,