A factorial typology is a set of grammars. We are not given the grammars directly, but must deduce them from the way that the posited constraints deal with the posited structures. How do we know that the candidate sets we have examined are sufficient to discriminate all the grammars that are allowed by our assumptions? This is the problem of finding a universal support for a typology. Without a universal support, we don't have the typology, and without the typology, many types of systematic claims about it must languish unjustified.Here we show how the universal status of a proposed support may be established when we have exact descriptions of the types of optima allowed in the grammars. If a typology is factored into (intensional) ranking properties in the sense of Alber & Prince (in prep.), and if the property values are associated with (extensional) characteristics carried by optima, then a grammar as a combination of values is associated with a description of its optima as a conjunction of the characteristics associated with the values. If the descriptions thereby obtained uniquely denote single candidates, then the grammars cannot be further refined, and the support that produced the grammars must be universal.This method of associating extensional characteristics with ranking patterns answers a much more general question: what do the languages of a typology look like? Since a typology is generated from a finite sample of candidate sets, we cannot in general be satisfied with remarking about the distribution of characteristics in the sample. We must use the grammars to project over the entire set of optima. The grammatical structure relevant to this enterprise is encoded in the ranking properties that combine to give the grammars.

Recent work under the theoretical banner of Agreement by Correspondence (ABC) has produced a variety of different – and sometimes contradictory – formulations of the constraints central to this framework. In OT, the effects of such definitional choices come out in the factorial typologies they predict. Yet knowing what languages a theoretical system derives is insufficient unless we know why it does so. This requires analysis of the internal ranking structures of the typology itself. This paper compares the typologies produced under different proposed modifications to the main ABC constraints. We analyse the typologies in Property Theory, a theory of typological organisation in OT. Our analyses show that all variations have a common core structure, and that differences in their factorial typologies reduce to differences in how this common structure expands and iterates for different features. This allows for precise delineation of how and why different ABC constraint definitions affect typologies.

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...

A learner's task is to find the most restrictive grammar consistent with the data of their language. This paper develops an OT learning algorithm that incorporates typological-level information from Property Analysis to increase restrictiveness and successfully learn subset languages. Based on Tesar's (2014) Output-Driven Learner (ODL), Property-ODL (PODL) uses ERCs taken from property values encoding specific markedness > faithfulness rankings. PODL was tested in a learning simulation for the phonological system in Tesar (2014), Paka, which presents the challenging case of languages in paradigmatic subset relations. In ODL, these require additional methods to be learned. PODL eliminates the need for these in learning the paradigmatic subsets and overall reduces the use of less-tested methods in learning the grammars of the typology.

The same linguistic data can often be analyzed in multiple ways, using different theoretical assumptions. Systematic comparison of the competing analyses requires understanding how the theories give rise to them, and the consequences and predictions implied by each set of assumptions. In this paper, we compare two theories of segmental harmony: Agreement-by-Correspondence (ABC) (Rose & Walker 2004; Hansson 2010; Bennett 2015), and Agreement-by-Projection (ABP) (Hansson 2014). We analyze typologies in each through Property Theory (Alber, DelBusso & Prince 2016; Alber & Prince 2016, in prep.). Typological analysis shows the strong parallelism between the different proposals at both the extensional and intensional levels. Not only do both theories predict the same set of surface distinct languages, but these follow from a similar internal structure. We show how the ABP proposal formally combines two ABC constraints, collapsing the ABC typology along the correspondence/noncorrespondence dimension.