INTRODUCTION

1.1. Sentences, rules, and grammars

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. 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 a derivation, which consists of a sequence of graph-theoretic objects called (not too happily) constituent structure trees. Secondly, a linguistic theory must have a conception of what a possible sentence-Specifying system or grammar is. This necessarily involves views about what a possible grammatical rule is, what a possible combination of grammatical rules (possible grammar) is, and a specification of how grammars characterize classes of sentences. Inevitably, the conception of the nature of a sentence will greatly determine what conception of grammatical rule is required, although the notion of rule adopted may (and normally will) feed back and determine in part the conception of linguistic object. Thus, it is the idea that grammatical structure involves a sequence of constituent structures (rather than the single structure of structuralist theories) which leads transformational theorists to a conception of grammatical rule countenancing grammatical transformations, etc. But the presumption that transformations exist has, in turn, led to many assumptions about sentence structure, e.g., that there are symbols which trigger transformations, elements like doom, traces, etc. As will become clear, the current work makes no use of the fundamental TG construct Derivation and a fortiori no use of those concepts dependent on or related to this central notion.

This work develops a new conceptual framework, which we call Arc Pair Grammar (henceforth: APG). APG is radically different from any other extant conception of linguistic theory along many but not all parameters. Although its concept of sentence structure is an outgrowth of largely unpublished work in RG (see section 1.3 for discussion of the recent historical antecedents of APG), APG will be about 95 percent new even to those familiar with work in RG. To those unfamiliar with the RG framework, APG will be essentially 100 percent novel.

Let us briefly contrast one current TG framework with that of APG. Within the current version of the so-called extended standard theory (of TG), a grammar is characterized in terms of various types of object, inter alia (see Chomsky and Lasnik [1977]): (i) a base containing a categorial component (context-free grammar generating an infinite set of phrase markers) and a lexicon (containing word formation and lexical redundancy rules); (ii) lexical insertion rules; (iii) a transformational component; (iv) a semantic interpretive component; (v) a deletion component; (vi) a surface filter component; (vii) a phonological interpretive component, and (viii) a stylistic component. Corresponding to this TG view of a grammar, sentence structure involves various levels of representation, roughly: (a) an initial phrase marker generated by (i); (b) a base phrase marker, generated by (ii); (c) a sequence of phrase markers or a derivation, generated by (iii), the last phrase marker being termed a surface structure, determined in part to be well-formed by (vi); (d) a logical form, generated by (iv); (e) a level determined by the output of (v); (f) a phonological form, generated by (vii), and (g) a final output generated by (viii).

In contrast, APG represents each natural language sentence in terms of a formal object called a Pair Network (PN). A PN is, from one viewpoint, a system involving four components: (i) an overall graph-theoretic object called a Relational Graph (R-graph), discussed in detail in Chapter 2; (ii) a graph-theoretic object which is a subpart of the overall R-graph in (i), called a Logical Graph (L-graph), discussed in detail in Chapter 4; (iii) a graph-theoretic object which is a subpart of the overall R-graph in (i) and distinct from the L-graph, called a Surface Graph (S-graph), also discussed in detail in Chapter 4; and (iv) two primitive relations called Sponsor and Erase, ranging over pairs of elements (called arcs) from R-graphs. These are discussed throughout this work from Chapter 5 on.

The APG construct L-graph is a formal characterization of the notion (linguistically motivated) logical form. The construct S-graph is roughly the formal characterization within APG of that aspect of sentence structure characterized in terms of Surface Structure in TG. The relations Sponsor and Erase and the laws and grammatical rules which refer to them are the APG explication not only of that aspect of sentence structure characterized in TG in terms of derivations and conditions on derivations, but also that aspect putatively characterized by interpretive components, stylistic components, etc. In short, the APG conception of grammar is far more homogeneous and monolithic than that of TG. It claims that there is a single web of notions relevant for describing all aspects of language, a claim in no way inconsistent with the existence of differentiating features of various subaspects. Thus, within APG there is no notion of, e.g., base component, lexical component, lexical insertion rules, transformational component, semantic interpretive component, deletion component, surface filter component, stylistic component, nor any of the other or associated constructs (cycles, rule ordering, traces, etc.) commonly assumed to be characterized in terms of, or held to apply to, the preceding aspects of TG.

A PN is simply a pairing of a Sponsor relation and an Erase relation such that (i) each relation is a set of ordered pairs of arcs, and (ii) the set of arcs formed by the domains and ranges of Sponsor and Erase (a) forms an R-graph and (b) has two subsets, one forming an L-graph and one forming an S-graph. Thus, R-graph, L-graph, and S-graph are derivative concepts, part of the defining criteria of the single formal objects called PNs.

Corresponding to the fundamental difference between the TG and APG notions of sentence structure are differences in the associated notions of grammatical rule and grammar. Unlike, e.g., transformations and other TG rules, APG grammatical rules do not map formal objects into formal objects via a specified set of operations. Rather, APG rules, like the laws of APG universal grammar (PN laws),...