Arc Pair Grammar

Arc Pair Grammar

David E. Johnson
Paul M. Postal
Copyright Date: 1980
Pages: 752
https://www.jstor.org/stable/j.ctt7ztvk9
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  • Book Info
    Arc Pair Grammar
    Book Description:

    Arc pair grammar is a new, extensively formalized, theory of the grammatical structure of natural languages. As an outgrowth of relational grammar, it constitutes a theoretical alternative to the long-dominant generative transformational approach to linguistics. In this work, David Johnson and Paul Postal offer the first comprehensive presentation of this theoretical framework, which provides entirely new notions of all the basic concepts of grammatical theory: sentence, language, rule, and grammar.

    Originally published in 1981.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-5555-1
    Subjects: Language & Literature

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-viii)
  3. PREFACE
    (pp. ix-2)
  4. CHAPTER 1 INTRODUCTION
    (pp. 3-28)

    Any linguistic theory must involve two basic interrelated conceptions.First,there must be a set of ideas about the nature of the basic elements of language,sentences.¹ Any such theory must have a basic conception of what kind of formal objects sentences are. For example, in all current variants of transformational theory (henceforth TG), sentences are regarded as quite complicated formal objects involving logical representations, phonological and phonetic representations, and a central core of structure called aderivation,which consists of a sequence of graph-theoretic objects called (not too happily)constituent structure trees.² Secondly, a linguistic theory must have a...

  5. CHAPTER 2 GRAPH-THEORETIC ASPECTS OF APG
    (pp. 29-59)

    As indicated in Chapter 1, in the APG framework, sentences are reconstructed in terms of formal objects referred to as PNs. In the present chapter, we introduce and develop those formal features of PNs which are, in effect, naturally describable in terms of objects studied in the branch of mathematics called graph theory.

    We begin by considering the primitive elements of the theory. PNs are formal objects which involveseven typesof primitive:

    (1) The Primitive Constructs Underlying PNs

    a. A denumerably infinite set, NTNo , of elements callednonterminal nodes.

    b. A (finite) set, LNo , of elements called...

  6. CHAPTER 3 ARC PAIR RELATIONS
    (pp. 60-74)

    In this chapter, we informally discuss the primitive relations, Sponsor and Erase. This discussion will serve as an introduction to the more ex tensive, formal development of the central notion PN, which involves the formal correspondents of Sponsor and Erase. As mentioned in Chapter 1, Sponsor and Erase are both binary relations holding between (in some cases unary) sequences of linguistic states. The basic idea behind these two concepts can perhaps be best understood by way of illustration.

    Consider:

    (1) John was kissed by Lois.

    Under our informal conception, the structure of (1) involves, in part, two linguistic levels, say...

  7. CHAPTER 4 PAIR NETWORKS
    (pp. 75-104)

    In Chapter 2, the concept R-graph was introduced and formally defined, and in the previous chapter, the Sponsor and Erase relations were informally and incompletely characterized. As previously stressed, the APG representation of a sentence, a PN, consists of a set with two members, one a Sponsor relation, the other an Erase relation. Each of these relations is a set of ordered pairs ofarcs,the latter concept formally defined in Chapter 2. Moreover, it has been informally mentioned that each PN has associated with it (i) an R-graph, which is the set of arcs “in” the PN, more precisely,...

  8. CHAPTER 5 BASIC SPONSOR AND ERASE LAWS
    (pp. 105-148)

    In the previous chapter, we defined the notion PN in terms of pairs of arcs in a Sponsor or an Erase relation and stated several conditions governing PNs. The present chapter introduces a variety of defined relations and states the basic laws governing the primitives, Sponsor, Erase, and the basic defined relations.

    In Chapter 2, we defined a number of relations between arcs, including Overlap, Neighbor, and Parallel. These are all reflexive, symmetric, and transitive relations, that is, equivalence relations. These relations are defined completely independently of the existence of Sponsor and Erase pairs in PNs, and merely in terms...

  9. CHAPTER 6 COORDINATE DETERMINATION
    (pp. 149-188)

    Chapter 1 mentioned that coordinates are the formal representation in APG terms of the informal notion of linguistic levels. Consider:

    (1) Tina saw Jack.

    HereTinais understood as the 1, andJackthe 2, of the clause having saw as the verb.¹ There is a single linguistic level whereTinaandJackbear, respectively, the 1 and the 2 relations. Internal to the APG formalism, this information is represented by a 1 arc with P-headTinaand a 2 arc with P-headJack,where both arcs share coordinate C1(the rationale for picking C1over other coordinates will become...

  10. CHAPTER 7 FOCUS ON CLAUSE STRUCTURE
    (pp. 189-271)

    The bulk of work in APG, as in stage 1 and stage 2 RG, has involved the study of clause structure, e.g., such topics as passivization, “raising,’ “reflexivization,” impersonal constructions, etc. Despite this, we have developed APG in extremely general terms, providing, we hope, the basic apparatus for the description of all aspects of grammatical structure. However, the overwhelming body of empirical research bearing on APG remains in the area of clause structure and most of the empirical results obtained lie in this domain. Thus, certain assumptions which we have framed in quite general terms are largely motivated by work...

  11. CHAPTER 8 CHO ARCS
    (pp. 272-358)

    The notionChômeuris one of the distinctive elements of both RG and APG, and a concept largely without antecedents in previous linguistic work.¹ Cho arcs, which formalize this concept in the present framework, are subject to a number of restrictive conditions separating them from other arcs.

    Informally, one can characterize Cho arcs as follows. Each Cho arc is either domestic or a graft. Graft Cho arcs are replacers, and locally sponsored by domestic Cho arcs. We essentially ignore graft Cho arcs in what follows since they follow the laws for grafts and are not otherwise notable. Domestic Cho arcs...

  12. CHAPTER 9 FURTHER PRINCIPLES GOVERNING THE DISTRIBUTION OF CHO ARCS
    (pp. 359-400)

    Chapter 8 did not deal with the problem of distinguishing between legal analyses like those in (8.30) and (8.31) and otherwise identical structures where UN and, e.g.,Maryare interchanged. The legal structures are given in (1), and the corresponding illegal analyses in (2):

    Our assumption is that both (2a, b) and all similar structures must be excluded from the class of well-formed PNs. However, since the corresponding structures of (1) and (2) differ only by the interchange of the nominals UN andMary,none of the laws so far proposed exclude the forms of (2). For none of these...

  13. CHAPTER 10 GHOST ARCS AND DUMMY NOMINALS
    (pp. 401-447)

    The recent linguistic literature contains many references todummy nominals,by which are meant such forms as those italicized in:

    (1) a.Thereare demons in Newark.

    b.Itfrightens me the things he does.¹

    c.Itis sleeting.

    d.Itis obvious that Tricky was guilty.

    e. French

    IlIui est arrivé un malheur.

    It to him/her is arrived a misfortune = “Something bad happened to him/her.”

    f. German

    Eskamen zwei junge leute.

    It came two young people = “two young people came.”

    g. Welsh

    Yr oeddhi ynbwrw glaw ddoe.

    was she rain throw yesterday =...

  14. CHAPTER 11 REPLACERS AND ANAPHORA
    (pp. 448-546)

    In this chapter, we sketch how the concept Replace contributes to solving various problems raised by a conception of “coreference” as involving overlapping self-sponsoring Nominal arcs. We develop the outlines of a theory of pronominal anaphora and show how it deals with certain issues in the domain of anaphoric connections. One result is that although there is clearly a “grammatical relation” representing anaphoric connections between elements, it is unnecessary in the APG framework to recognize a primitive to represent this relation. This is so because it is possible to provide an effective definition of the anaphoric relation in terms of...

  15. CHAPTER 12 LINEAR PRECEDENCE
    (pp. 547-601)

    That there is a relation of linear precedence in natural language is one point on which all linguists surely agree. But disagreements arise when it comes to specifying the nature and overall role of such a relation in linguistic theory.

    It is in a sense traditional to sharply differentiate linear precedence from so-called “grammatical relations,” like subject, indirect object, modifier, etc. This distinction is codified in TG, where linear precedence forms one of the three primitive relations of sentence structure (along with labeling and constituency), while all other grammatical relations are either taken as defined, or rejected. Our own view...

  16. CHAPTER 13 GRAFTS, PIONEERS, AND CLOSURES
    (pp. 602-654)

    The present chapter sketches how APG notions can provide the outlines of an account of various standard grammatical features including prepositional and postpositional flagging, case marking, and the structures involved in phenomena like Heavy NP Shift. Basic to the treatment of these is the notion Graft, applied in Chapter 11 to anaphora and in Chapter 12 to linear precedence, and a subtype of immigrant arc we refer to aspioneers.

    Consider prepositional flagging, the structure of basic prepositional phrases like that italicized in:

    (1) Melvin spoke to Gladys.

    Ignoring sponsor and erase pairings, we suggest that such phrases have the...

  17. CHAPTER 14 APG RULES AND GRAMMARS
    (pp. 655-714)

    Chapters 1 through 13 have partially developed and motivated that aspect of APG theory dealing with the notionpossible PN in a natural language,orPN well-formed at the level of APG universal grammar.Such PNs are those which could in principle be well formed in some natural language. Informally, a PN is of this character if and only if itsatisfies¹ all the PN laws. Since PN laws are interpreted as material implications in the ordinary logical sense, this is to say the following: a PN, PNu, is well formed at the level of universal grammar just in case...

  18. REFERENCES
    (pp. 715-723)
  19. INDEX
    (pp. 724-739)
  20. Back Matter
    (pp. 740-740)