Variable affix order: Grammar and learningKevin M. RyanLanguage, Volume 86, Number 4, December 2010, pp. 758-791 (Article)Published by Linguistic Society of AmericaFor additional information about this article Access Provided by UCLA Library at 04/05/11 5:51PM GMThttp://muse.jhu.edu/journals/lan/summary/v086/86.4.ryan.html758VARIABLE AFFIX ORDER: GRAMMAR AND LEARNINGKevin M. RyanUniversity of California, Los AngelesWhile affix ordering often reflects general syntactic or semantic principles, it can also be arbi-trary or variable. This article develops a theory of morpheme ordering based on local morphotac-tic restrictions encoded as weighted bigram constraints. I examine the formal properties ofmorphotactic systems, including arbitrariness, nontransitivity, context-sensitivity, analogy, andvariation. Several variable systems are surveyed before turning to a detailed corpus study of a vari-able affix in Tagalog. Bigram morphotactics is shown to cover Tagalog and the typology, whileother formalisms, such as alignment, precedence, and position classes, undergenerate. Moreover,learning simulations reveal that affix ordering under bigram morphotactics is subject to analogicalpressures, providing a learning-theoretic motivation for the specific patterns of variation observedin Tagalog. I raise a different set of objections to rule-based approaches invoking affix movement.Finally, I demonstrate that bigram morphotactics is restrictive, being unable to generate unattestedscenarios such as nonlocal contingency in ordering.*Keywords: affix order, morphotactics, morphology, variation, TagalogThough the order in which morphemes are realized within a word is sometimespredictable on general syntactic or semantic grounds, ordering can also be subject tolanguage-specific constraints, or exhibit free variation. Without denying the roles of theinterfaces in affix ordering, this article focuses on the grammar and learnability of its ar-bitrary aspects. The theory of morphotactics must cover phenomena such as countersco-pal or otherwise arbitrary ordering restrictions, nontransitivity (e.g. X-Y [*Y-X] and Y-Z[*Z-Y], but Z-X [*X-Z]), context-sensitivity (e.g. X-Y-A [*Y-X-A] but Y-X-B [*X-Y-B]), gradient variation, learnability, and analogical effects (§6). For some of these phe-nomena, only a subset of logically possible patterns is found in human languages (e.g.context-sensitivity in ordering is always local). The theory should therefore also be re-strictive, generating only possible patterns. I argue that morphotactics are encoded lo-cally, as adjacency bigrams, while other proposals—such as morpheme alignment,precedence constraints, position classes, templates, and affix movement—critically un-dergenerate or overgenerate.Gradient variation in affix ordering is a particularly stringent testing ground for mor-photactic theories. I flesh out the typology of affix-order variation with cases from sev-eral languages before turning to the primary case study of this article, Tagalog’saspectual reduplicant (Schachter & Otanes 1972 (hereafter S&O), Carrier 1979, Con-doravdi & Kiparsky 1998, Rackowski 1999, Mercado 2007, Skinner 2008). Building onprevious accounts with a corpus study, I discuss the productive characteristics of thesystem, including its gradience (not all options are equally good) and the sorts of mor-phological contingencies the morphotactic grammar must address. A sample of Tagalogdata follows in 1–4 as a brief illustration of such gradience and contingency (see §3 fordetails). First, individuals freely place aspectual ‘RED’ before or after the causative pre-fix pa, as in 1. The corpus incidence of the affix matrix (with RED in any position) andpercentages of the variants appear to the right. As discussed in §3, the variants’ propor-tions are generally consistent across roots.* I wish to thank Kie Zuraw, Bruce Hayes, Hilda Koopman, Laura McPherson, Joe Pater, Colin Wilson, au-diences at UCLA, UC Berkeley, and the LSA annual meeting, the editors, and three anonymous referees fortheir insightful questions, criticisms, and suggestions. I also thank Larry Hyman and Sam Mchombo for theirassistance with the Chichewa data. All faults are my own. This material is based on work supported by a Na-tional Science Foundation Graduate Research Fellowship.VARIABLE AFFIX ORDER 759(1) ~ pa- RED -ROOT-an (64.5%)~ RED -pa-ROOT-an (35.5%) (N = 212,140)When pag ‘transitive’ is added outside of pa as in 2, however, the position after pa isalmost never employed. (Variants whose corpus proportions round to 0.0% are notshown.) Third, the position between pag and pa continues to be the preferred variant(though more weakly so) when two additional prefixes, ma ‘ability’ and ʔi ‘object top-ic’, are added to the prefix string in 2 to make 3. Finally, when ʔi, the second prefix in3, is replaced with ka ‘telic’ in 4, a higher position in the verb, between ma and ka, ispreferred.(2) ~ pag- RED -pa-ROOT (100%) (N = 880,685)(3) ~ ma-ʔi-pag- RED -pa-ROOT (96.0%)~ ma-ʔi- RED -pag-pa-ROOT (4.0%) (N = 3,073)(4) ~ ma-ka-pag- RED -pa-ROOT (25.4%)~ ma- RED -ka-pag-pa-ROOT (74.6%) (N = 43,623)I demonstrate that these sorts of ‘free’ variation in Tagalog and other languages canbe modeled by a morphotactic grammar containing weighted bigram constraints, whicheffectively encode the relative coherences of pairs of cooccurring morphemes. Outputcandidates exhibiting all ordering permutations are evaluated by the constraint set fortheir global morphotactic harmonies, which can be translated into probabilities. In alearning simulation based on the comprehensive corpus data, the bigram learner closelymatches both the categorical and gradient properties of its Tagalog training data.One important finding of this article is that the set of marked (grammatical but notpreferred) variants in Tagalog is predictable from the set of unmarked (preferred) vari-ants. When the bigram learner is trained on the Tagalog corpus with all marked variantsremoved, the learner overgenerates variation in patterns that resemble the unseen actualcorpus, both in terms of the positions that are overgenerated and the degrees to whichthey are overgenerated. I am therefore able to motivate the evolution and stability ofsuch a complex morphotactic system. The variation, I suggest, is driven by the over-generalization of local morphotactics, a kind of analogy in affix