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<Paper uid="J98-2003">
  <Title>nian Academy</Title>
  <Section position="2" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
1. Introduction
</SectionTitle>
    <Paragraph position="0"> Contextual grammars were introduced by Marcus (1969), as &amp;quot;intrinsic grammars,&amp;quot; without auxiliary symbols, based only on the fundamental linguistic operation of inserting words in given phrases, according to certain contextual dependencies. More precisely, contextual grammars include contexts (pairs of words), associated with * University of Bucharest, Faculty of Mathematics, Str. Academiei 14, 70109 Bucharest, Romania. E-mail: solomon@imar.ro t Research Group on Mathematical Linguistics and Language Engineering (GRLMC), Rovira i Virgili University, P1. Imperial Thrraco 1, 43005 Tarragona, Spain. E-maih cmv@astor.urv.es Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, 70700 Bucharest, Romania. E-mail: gpaun@imanro. Research supported by the Academy of Finland, project 11281, and Spanish Secretaria de Estado de Universidades e Investigaci6n, grant SAB 95-0357.</Paragraph>
    <Paragraph position="1"> @ 1998 Association for Computational Linguistics Computational Linguistics Volume 24, Number 2 selectors (sets of words); a context can be adjoined to any associated word-selector. In this way, starting from a finite set of words, we can generate a language.</Paragraph>
    <Paragraph position="2"> This operation of iterated selective insertion of words is related to the basic combinatorics on words, as well as to the basic operations in rewriting systems of any type. Indeed, contextual grammars, in the many variants considered in the literature, were investigated mainly from a mathematical point of view; see P~iun (1982, 1985, 1994), P~un, Rozenberg and Salomaa (1994), and their references. A complete source of information is the monograph P~iun (1997). A few applications of contextual grammars were developed in connection with action theory (P~un 1979), with the study of theatrical works (P~iun 1976), and with computer program evolution (B~lanescu and Gheorghe 1987), but up to now no attempt has been made to check the relevance of contextual grammars in the very field where they were motivated: linguistics, the study of natural languages. A sort of a posteriori explanation is given: the variants of contextual grammars investigated so far are not powerful enough, hence they are not interesting enough; what they can do, a regular or a context-free grammar can do as well. However, a recently introduced class of contextual grammars seems to be quite appealing from this point of view: the grammars with a maximal use of selectors (Martin-Vide et al. 1995). In these grammars, a context is adjoined to a word-selector if this selector is the largest on that place (no other word containing it as a proper subword can be a selector). Speaking strictly from a formal language theory point of view, the behavior of these grammars is not spectacular: the family of generated languages is incomparable with the family of context-free languages, incomparable with many other families of contextual languages, and (strictly) included in the family of context-sensitive languages, properties rather common in the area of contextual grammars.</Paragraph>
    <Paragraph position="3"> This type of grammar has a surprising property, however, important from a linguistic point of view: all of the three basic features of natural (and artificial) languages that lead to their non-context-freeness (reduplication, crossed dependencies, and multiple agreements) can be covered by such grammars (and no other class of contextual grammars can do the same). Technically, the above mentioned non-context-free features lead to formal languages of the forms {xcx I x E {a, b}*} (duplicated words of arbitrary length), {anbmcnd m I n, m &gt; 1} (two crossed dependencies), and {anbnc&amp;quot; I n &gt; 1} (\[at least\] three correlated positions). All of them are non-context-free languages and all of them can be generated in a surprisingly simple way by contextual grammars with selectors used in the maximal mode.</Paragraph>
    <Paragraph position="4"> Examples of natural language constructions based on reduplication were found, for instance, by Culy (1985), and Radzinski (1990), whereas crossed dependencies were demonstrated for Swiss German by Shieber (1985); see also Partee, ter Meulen and Wall (1990) or a number of contributions to Savitch et al. (1987). Multiple agreements were identified early on in programming languages (see, for example, Floyd \[1962\]), and certain constructions having such characteristics can also be found in natural languages. We shall give some arguments in Section 4.</Paragraph>
    <Paragraph position="5"> Some remarks are in order here. Although we mainly deal with the syntax of natural languages, we sometimes also mention artificial languages, mainly programming languages. Without entering into details outside the scope of our paper, 1 we adopt the standpoint that natural and artificial languages have many common features (Man-</Paragraph>
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