Abstract
We discuss a set-theoretic treatment of segments as sets of valued features and of natural classes as intensionally defined sets of sets of valued features. In this system, the empty set { } corresponds to a completely underspecified segment, and the natural class [ ] corresponds to the set of all segments, making a feature ± Segment unnecessary. We use unification, a partial operation on sets, to implement feature-filling processes, and we combine unification with set subtraction to implement feature-changing processes. We show how unification creates the illusion of targeting only underspecified segments, and we explore the possibility that only unification rules whose structural changes involve a single feature are UG-compatible. We show that no such Singleton Set Restriction can work with rules based on set subtraction. The system is illustrated using toy vowel harmony systems and a treatment of compensatory lengthening as total assimilation.
Highlights
Developing ideas introduced in Bale et al (2014) and Bale and Reiss (2018), this paper explores some of the consequences of analyzing segments as sets of features and, as a corollary, analyzing natural classes as sets of sets of features
We argue that complete assimilation is best treated by decomposing the traditional arrow of phonological rules into two separate operations, one that involves feature deletion and another that uses unification
Our set-theoretic treatment of segments provides mechanisms to address the problem of referring to underspecified segments, including the empty segment, while still maintaining the principle that rules target natural classes
Summary
Developing ideas introduced in Bale et al (2014) and Bale and Reiss (2018), this paper explores some of the consequences of analyzing segments as sets of features and, as a corollary, analyzing natural classes as sets of sets of features. Bale et al (2014) introduce an innovation to phonological notation to better reflect the type-theoretic nature of the components of rules, based on the idea that segments are consistent sets of valued features, that is, sets that may contain +F or −F, for a given feature F, but not Extrapolating from the impossibility of referring to /D/ (without /t/ and /d/), which is underspecified only for Voiced, it follows that no rule can target a segment p whose representation contains a subset of the information in the representation of a segment q, without targeting q Pushing this to the logical limit, what happens if a segment corresponds to the empty set of valued features, the fully underspecified segment, which we denote as { }? Independent of the merits of any prior arguments for or against this feature, we see that a set theoretic representation of targets in which natural classes are represented as sets of sets vitiates the need for a +Segment feature
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