Some classes of sets of structures definable without quantifiers

Abstract

We derive abstract characterizations of the Strictly Piecewise Local (SPL) and Piecewise Locally Testable (PLT) stringsets. These generalize both the Strictly Local/Locally Testable stringsets (SL and LT) and Strictly Piecewise/Piecewise Testable stringsets (SP and PT) in that SPL constraints can be stated in terms of both adjacency and precedence.We do this in a fully abstract setting which applies to any class of purely relational models that label the points in their domain with some finite labeling alphabet. This includes, for example, labeled trees and graphs. The actual structure of the class of intended models only shows up in interpreting the abstract characterizations of the definable sets in terms of the structure of the models themselves.

Typology emerges from simplicity in representations and learning

“…In other words, we would expect linguistic typology to inhabit only the lower regions of the hierarchy, or at least be biased heavily toward this region. Rogers and Lambert (2019b) provide strong evidence that this is in fact the case when it comes to stress patterns. Their exhaustive analysis of the more than one hundred stress patterns in the StressTyp2 database (Goedemans et al 2015) showed [ 175 ] that each of these can be described as the interaction of constraints that can be learned by Algorithms I and II.…”

Relativized Adjacency

“…Under this modeltheoretic view, the relativized successor relation ◁ T is parameterized by the alphabet over which it is relativized, so different instantiations of this relation are as different as the ◁ and < relations. With this in mind, future work in understanding these interactions will shed light on the strictly piecewise-local class discussed in Rogers and Lambert (2019b), and vice-versa. Moreover, Aksënova and Deshmukh (2018) discuss attested interactions of multiple tiers; one might ask which kinds of combinations (if any) allow intersection-closure to be maintained.…”