ABA and the combinatorics of morphological features

Glossa a journal of general linguistics Bobaljik, Jonathan David and Uli Sauerland. 2018. *ABA and the combinatorics of morphological features. Glossa: a journal of general linguistics 3(1): 15. 1–34, DOI: https://doi.org/10.5334/gjgl.345 RESEARCH *ABA and the combinatorics of morphological features Jonathan David Bobaljik1 and Uli Sauerland2 1 University of Connecticut and Leibniz-Zentrum Allgemeine Sprachwissenschaft (ZAS), Storrs, CT, USA and Berlin, DE 2 Leibniz-Zentrum Allgemeine Sprachwissenschaft (ZAS), Berlin, DE Corresponding authors: Jonathan David Bobaljik (), Uli Sauerland () In several three cell paradigms, it has been observed that one logically conceivable pattern – ABA under some arrangement of cells – is unattested. Existing approaches assume that such *ABA generalizations provide evidence for feature inventories which are restricted to features that stand in containment relations, and are thus subject to Pāṇinian rule order. We present a novel approach to *ABA generalizations that derives from general properties of feature-based morphology. To this end, we develop a formal account of the widespread view that morphological paradigms derive from rules that relate abstract features from an inventory to morphological exponents. We demonstrate that the feature-based view restricts the space of typological patterns even without any further assumptions. We show furthermore that the feature-based theory derives *ABA as a special case of a broader class of generalizations if the number of features in the inventory must be minimal, and that these generalizations arise under a variety of general assumptions about feature-algebras (extrinsically ordered or Pāṇinian and with or without feature intersection). We discuss which explanation might be correct for actual cases of *ABA constraints, and we explore the consequences of the feature-based general approach for a range of paradigm sizes including those with more than three cells. Keywords: features; morphology; combinatorics; syncretism; typology 1 Introduction One of the most interesting and difficult questions in research on language lies in formally characterizing the class of possible grammars. One aspect of this challenge asks whether there are constraints on grammars of a general, abstract nature, and in turn, whether these constraints are specific to language or instantiations of even broader, domain-general constraints on cognitive systems, with manifestations observable elsewhere. For example, some progress has been made in syntax on the basis of Formal Language Theory and the Chomsky Hierarchy (Chomsky 1956) for the analysis of sets of string sequences. We aim to contribute to the development of a similarly general perspective for morphology, particularly with respect to morphological features, i.e. the features that underlie the variation in how different concepts are grouped across languages as evidenced by exponence by the same form (syncretism). The architecture of feature-based morphological systems predicts that only certain patterns of variation are possible. In this paper, we address *ABA generalizations from this perspective. We show that a class of *ABA-type generalizations can be derived from the feature-based architecture in conjunction with a minimality assumption. We furthermore argue that such a derivation may be plausible for some cases of an *ABA generalization, but not for others. The term *ABA generalization refers to morphological patterns in which, given some arrangement of the relevant forms in a structured sequence, the first and third may share Art. 15, page 2 of 34 Bobaljik and Sauerland: *ABA combinatorics some property “A” only if the middle member shares that property as well. If the middle member is distinct from the first, then the third member of the sequence must also be distinct. Bobaljik (2012) demonstrates that a *ABA generalization holds for adjectival suppletion in the sequence positive-comparative-superlative: across a large cross-linguistic sample, one finds ABB patterns such as good-better-best, where the comparative and superlative share a root be(t)- distinct from the positive, but what is not found is an ABA pattern: *good-better-goodest, in which the positive and superlative share a root, distinct from the comparative. Similar *ABA effects have been noted in extensive studies of case syncretism (Caha 2009), suppletion for both case and number in pronouns (Smith et al. 2016), Germanic verbs and participles (see Wiese 2008 on German, and class material cited by Starke 2009 on English), and in other domains. In one way or another, almost all existing accounts of these generalizations have argued that the *ABA effect arises as a result of nesting or containment relations among features, along with the assumption that linguistic rules are arranged such that a more specific rule takes precedence over (bleeds) a more general one, the so-called Elsewhere or Pāṇinian ordering (Kiparsky 1973; 1979). For the example above, Bobaljik argues that the representation of the superlative properly contains the representation of the comparative, which in turn properly contains the basic form of the adjective, as in (1). (1) a. b. c. Positive: [adjective] Comparative: [[adjective] comparative] Superlative: [[[adjective] comparative] superlative] If a language has a rule of suppletion such as good ↦ be(t)- / __ comparative, that rule will block the basic root good in both the comparative and the superlative, in virtue of being the most specific rule compatible with the context. Nothing forces the comparative and superlative to share a root – Latin uses an ABC pattern (bonus-melior-optimus) with a distinct root in each of the three grades, but the containment relation in (1) ensures that the ABA pattern is underivable (except as a case of accidental homophony).1 In this paper, we discuss some results of an ongoing project studying the combinatorial properties of rule systems that describe syncretism in morphological paradigms. Although that project did not set out to examine *ABA patterns per se, it turns out that *ABAlike restrictions emerge as a quite general prediction from the assumption that Universal Grammar selects the minimal feature inventories needed to generate a paradigm of a given size. We call this the assumption of Minimality. We present both a general and a narrow version of this restriction. The narrow, more specific prediction arises if we assume that feature intersection is permitted in the formulation of rules of exponence. We believe this narrow result is particularly interesting, since the *ABA restriction emerges without the containment/nesting hypothesis that characterizes other accounts. Intuitively, *ABA emerges when a three-element sequence is the product of two overlapping features and their intersection: in the sequence (“paradigm”) x,y,z, if x and y share a feature, and y and z share a feature, but x and z do not share a feature, the (...truncated)