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11
The Equivalence Of Four Extensions Of ContextFree Grammars
 Mathematical Systems Theory
, 1994
"... There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This paper concerns the relationship between the class of string languages generated by several such formalisms viz. Combinatory Categorial Grammars, Head Grammar ..."
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Cited by 79 (5 self)
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There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This paper concerns the relationship between the class of string languages generated by several such formalisms viz. Combinatory Categorial Grammars, Head Grammars, Linear Indexed Grammars and Tree Adjoining Grammars. Each of these formalisms is known to generate a larger class of languages than ContextFree Grammars. The four formalisms under consideration were developed independently and appear superficially to be quite different from one another. The result presented in this paper is that all four of the formalisms under consideration generate exactly the same class of string languages. 1 Introduction There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This is based on the argument that a grammar formalism should not merely be viewed as a notation, but as part o...
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.
Grammar Formalisms Viewed as Evolving Algebras
 Linguistics and Philosophy
, 1994
"... We consider the use of evolving algebra methods of specifying grammars for natural languages. We are especially interested in distributed evolving algebras. We provide the motivation for doing this, and we give a reconstruction of some classical grammatical formalisms in directly dynamic terms. Fina ..."
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Cited by 8 (0 self)
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We consider the use of evolving algebra methods of specifying grammars for natural languages. We are especially interested in distributed evolving algebras. We provide the motivation for doing this, and we give a reconstruction of some classical grammatical formalisms in directly dynamic terms. Finally, we consider some technical questions arising from the use of direct dynamism in grammatical formalisms. 1 Introduction Formal work in linguistics has both produced and used important mathematical tools. It led to formal language theory, and later developments in that field have found their way back to linguistics. But in addition, ideas originally developed for other applications have been incorporated into linguistic research. This paper considers the use of techniques from the theory of evolving algebras (see Gurevich [5]) in the development of syntactic formalisms. Our application of evolving algebras to grammatical formalisms may be viewed as part of several trends. First, there ha...
The Relationship Between Tree Adjoining Grammars And Head Grammars
, 1986
"... We examine the relationship between the two grammatical formalisms: Tree Adjoining Grammars and Head Grammars. We briefly investigate the weak equivalence of the two formalisms. We then turn to a discussion comparing the linguistic expressiveness of the two formalisms. ..."
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Cited by 5 (1 self)
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We examine the relationship between the two grammatical formalisms: Tree Adjoining Grammars and Head Grammars. We briefly investigate the weak equivalence of the two formalisms. We then turn to a discussion comparing the linguistic expressiveness of the two formalisms.
Iterative Learning of Simple External Contextual Languages
"... Abstract. It is investigated for which choice of a parameter q, denoting the number of contexts, the class of simple external contextual languages is iteratively learnable. On one hand, the class admits, for all values of q, polynomial time learnability provided an adequate choice of the hypothesis ..."
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Cited by 5 (2 self)
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Abstract. It is investigated for which choice of a parameter q, denoting the number of contexts, the class of simple external contextual languages is iteratively learnable. On one hand, the class admits, for all values of q, polynomial time learnability provided an adequate choice of the hypothesis space is given. On the other hand, additional constraints like consistency and conservativeness or the use of a oneone hypothesis space changes the picture — iterative learning limits the long term memory of the learner to the current hypothesis and these constraints further hinder storage of information via padding of this hypothesis. It is shown that if q> 3, then simple external contextual languages are not iteratively learnable using a class preserving oneone hypothesis space, while for q = 1 it is iteratively learnable, even in polynomial time. It is also investigated for which choice of the parameters, the simple external contextual languages can be learnt by a consistent and conservative iterative learner. 1
Evolving Algebras and Mathematical Models of Language
 Handbook of Logic and Language. North
, 1995
"... We consider the use of evolving algebra methods of specifying grammars for natural languages. We are especially interested in distributed evolving algebras. We provide the motivation for doing this, and we give a reconstruction of some classical grammatical formalisms in directly dynamic terms. Fina ..."
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Cited by 3 (2 self)
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We consider the use of evolving algebra methods of specifying grammars for natural languages. We are especially interested in distributed evolving algebras. We provide the motivation for doing this, and we give a reconstruction of some classical grammatical formalisms in directly dynamic terms. Finally, we consider some technical questions arising from the use of direct dynamism in grammatical formalisms. 1 Introduction Formal work in linguistics has both produced and used important mathematical tools. It led to formal language theory, and later developments in that field have found their way back to linguistics. But in addition, ideas originally developed for other applications have been incorporated into linguistic research. This paper considers the use of techniques from the theory of evolving algebras (see Gurevich [5]) in the development of syntactic formalisms. Our application of evolving algebras to grammatical formalisms may be viewed as part of several trends. First, there ha...
Bounded FixedPoint Definability and Tabular Recognition of Languages
, 1995
"... By relating positive inductive definitions to spacebounded computations of alternating Turing machines, Rounds, Comp. Linguistics 14, 1988, has given uniform grammatical characterizations of the EXPTIME and PTIME languages. But his proof gives fairly poor bounds for language recognition with contex ..."
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Cited by 1 (1 self)
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By relating positive inductive definitions to spacebounded computations of alternating Turing machines, Rounds, Comp. Linguistics 14, 1988, has given uniform grammatical characterizations of the EXPTIME and PTIME languages. But his proof gives fairly poor bounds for language recognition with contextfree resp. head grammars. We improve Rounds' analysis in two respects: first, we introduce a modified class of language definitions that allow restricted forms of negative inductions, and second, we show how to build tabledriven recognizers from such definitions. For a wide and natural class of language definitions we thereby obtain fairly efficient recognizers; we can recognize the boolean closure of contextfree resp. head languages in the wellknown O(n 3 ) resp. O(n 6 ) steps on a RAM . Our `bounded' fixedpoint formulas apparently can not define an arbitrary PTIME language. Our method is based on the existence of fixedpoints for a class of operators that need neither be mono...
Formal Properties of Categorial Grammars
, 2005
"... We discuss two standard formal tools used to study models of grammar. One of these is formal language theory, which provides a way to describe the complexity of languages in terms of a sequence of standard language classes known as the Chomsky hierarchy. The other tool is learnability theory, which ..."
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We discuss two standard formal tools used to study models of grammar. One of these is formal language theory, which provides a way to describe the complexity of languages in terms of a sequence of standard language classes known as the Chomsky hierarchy. The other tool is learnability theory, which can describe, for a given class of languages, whether or not there exists a single learner that can learn every language in the class; we use a particular model for learning developed by Gold. These two tools can be used to obtain formal properties of a grammar system, and to evaluate the validity of a theory of natural language. After presenting the tools, we show how they can be applied to the linguistic theory of categorial grammars, and we discuss the results. 1