Universals Across Languages

One motivation for model theoretic approaches to syntax is the prospect of enabling us to “abstract fully away from the details of the grammar mechanism – to express syntactic theories purely in terms of the properties of the class of structures they license” (Rogers, 1996). This is a worthy goal: in order to see the significant relations among expressions and their parts more clearly, and to describe similarities among different structures and different languages, we would like to discard those aspects of generative, derivational history which appear just because of our decision to use some particular generative device to specify it. If this is our goal, then although it is known that the derivation trees (or derived trees, or other closely related sets of structures) of various generative formalisms can be defined model-theoretically (Büchi, 1960; Thatcher and Wright, 1968; Doner, 1970; Thomas, 1997), that is not generally what we want. We want something more abstract; we want structures that “abstract fully away from . . . the grammar mechanism.” What are those structures? This paper takes some first, standard steps towards an algebraic, group-theoretic perspective on this question. A generative grammar can be given by a lexicon Lex and some generating functions F , defining the language L which is the closure of Lex with respect to F . The structure building functions of most grammars are partial, that is, they apply to some but not other expressions, and typically the domains of the functions are picked out by “syntactic categories” and “syntactic features.” This partiality is a very important part of grammar! Since the structure building rules in F define the structure of the language, we set the stage for our analysis by requiring the grammars to be “balanced” in a sense defined below, with rules F that are neither too specific nor too general. (Few of the grammars popular in mainstream syntax are balanced in this sense, but balanced formulations can be defined.) Then, in a first step towards a suitably abstract perspective, define the structural elements of a language (lexical items, properties, relations) to be those that are fixed by every automorphism of (L,F ). Two expressions then have the “same structure” if some automorphism maps one to the other. The automorphisms of course form a group with respect to composition, and so we have an instance of the familiar framework for the study of symmetries (Klein, 1893). This perspective stands well away from particular grammars with which we started, in a number of senses that we briefly explore. Although it conforms at many points with linguists’ intuitions about structure, a derivation tree of a particular gram-