Formally mapping the typologies of interacting ABCD systems

Abstract

ABCs of ABCDThe theory of Agreement By Correspondence has gained prominence as a way to explain harmony patterns, especially long-distance consonant agreement (Rose & Walker 2004, Hansson 2010. Bennett (2015) observes that the theory also generates Dissimilation, even with no further assumptions made (ergo 'ABCD'). This connection between dissimilation and assimilation is an appealing result, as it was in a large body of previous work that draws on the same mechanisms for both kinds of patterns (Mester 1986, Yip 1988.Recent work along ABCD lines has developed a range of varying formalizations. One point of variation is the correspondence relation at the heart of the theory, and the formal properties of it: is all correspondence homogenous? Is the relation transitive? Is it symmetric? Accompanying such questions are differences in the formal character of the constraints that refer to the correspondence relation: are agreement violations calculated over whole forms, or locally, based on pairs of correspondence? These points of difference definitively affect the typologies that result -particularly for situations where correspondence and/or agreement constraints based on multiple different features may conflict. Previous work has demonstrated as much through analyses of specific cases that seem to work far better in one version than others.1 But the analysis of individual case studies is not the most pressing question for the modern theorist: the much more important question is which of these different ABCD formulations makes the right typological predictions. Any answer to that question presupposes that we know what the typological predictions are. This is far from simple: all of the various formulations of ABCD are intended to generalize across different features, resulting in fairly large sets of constraints. Moreover, demonstrating all the effects of such constraints requires consideration of multiple segmental forms, with multiple correspondence structures available for each. The result is that we are comparing systems that are sufficiently large that their predictions cannot be deduced from intuition alone. This paper takes a step towards that goal. Our aim is to understand the interaction of two ABCD subsystems. Breaking the theory down into sub-systems, helpfully, models a key point of interest in comparing competing formulations. Many of the known differences between different ABCD formulations emerge from the interaction of two distinct ABCD effects (='ABCDE's: harmony or dissimilation patterns). So, if we want to understand the full predictions of any ABCD theory, we must know what possibilities it admits for the relationship between two harmony/dissimilation systems based on different features.The rest of the paper is organized in the following way. Section 2 defines the sub-systems analyzed here -the candidates and constraints included in each. These are modeled on a real-world point of departure, in the form of Kinyarwanda -a language with harmony among sibilants, and dissimilation between voiceless o...

ABP and ABC: Agreement with/out correspondence

“…Such bot structures also characterize ABC systems generally. Relative ranking of CORR and CC.ID constraints does not affect the choice of optima when both dominate the relevant faithfulness constraint(s) (Bennett & DelBusso 2018a;Bennett 2016;Bennett, DelBusso & Iacoponi 2016; see §3.2). The typology is structured around two subPAs, subsets of properties that form units in the full PA that determine the optimal mappings for different (sets of) inputs.…”

The typological effects of ABC constraint definitions

“…Each grammar is named 'C-bot', where C is the bottom-ranked constraint in all hierarchies consistent with the grammar, following the terminology of Merchant & Prince (2016). This ranking structure is shown to be characteristic of grammars in ABC(D) systems in Bennett et al (2016) (see also Bennett 2015: 75). In CORR-bot, all optima are faithful and do not correspond; they violate CORR, but not f.IO or CC.ID.…”

“…First, we show that all ABC systems have a general shared structure, arising from a basic interaction among the central constraint types. We analyse this structure within Property Theory (see Alber et al 2016 and Alber & Prince in preparation; also Bennett et al 2016, McManus 2016 and Alber & Prince 2017 for work within this theory). Property Theory provides the analytical framework needed to understand how the formal components – Gen and Con – give rise to a theory's typological predictions.…”

The intensional and the extensional properties of Headed Agreement By Correspondence

“…Second, as shown in Alber and Prince (in prep.) and in Bennett, DelBusso and Iacoponi (2016), the study of the properties of a system is useful when the system is extended to include more constraints or candidates. Finding the basic structure of a typology not only deepens our understanding of the theory, but it also significantly facilitates the analysis of its extended sub-systems, allowing us to rigorously study the effect the different components (such as classes of candidates or specific constraints) have on the theory.…”