Positional licensing, asymmetric trade-offs and gradient constraints in Harmonic Grammar

Abstract

In Harmonic Grammar, positional licensing interacts with faithfulness constraints in pathological ways: spreading a feature to a licensing position to satisfy positional licensing can incur many faithfulness violations, and if there are sufficiently many such violations, they gang up to block spreading. This problem is solved if positional licensing is recast as a positive constraint that rewards licensed features in proportion to the number of positions they are associated with, thereby countering faithfulness's multiple violations. This proposal provides support for positive constraints, calls into question arguments against gradient constraints and lays the groundwork for a sound theory of positional licensing in Harmonic Grammar.

Overshoot in licensing-driven harmony

“…Overshoot in Tudanca Montañés therefore has important theoretical consequences. It provides further support for PG-PL beyond the pathology-avoidance properties discussed by Kaplan (2018a), and it provides evidence that the proper way to prevent overshoot where necessary is through constraints that counter PL's incentive for overshoot, not by eliminating that incentive.…”

“…In Kaplan (2018a), I show that, while PL provides a satisfactory account of Tudanca Montañés-like harmony in Optimality Theory (OT; Prince & Smolensky 1993), it is deeply pathological in Harmonic Grammar (HG; e.g. Legendre et al 1990).…”

“…The reward assigned by this constraint increases as [―ATR] spreads to more positions. This gradience is central to resolving the pathologies that Kaplan (2018a) is concerned with, and positivity addresses certain problems introduced by gradience (Kimper 2011).…”

“…Kimper puts forth the only remedy for this problem I am aware of: serial derivations do not suffer from infinite goodness, because epenthesis and harmony must occur on separate steps, and, without the reward for harmony, there is no motivation for epenthesis in the first place. Kaplan (2018a) argues that for this reason the formalism in (4) requires serialism, but because that issue is tangential to present concerns, I use simpler parallel analyses here. Nothing of substance hinges on this choice: essentially, instead of harmony occurring in one fell swoop, a serial analysis targets one vowel at a time, with the same crucial constraint interactions that are present under parallel analyses.…”

“…Some harmony patterns analysed by Walker do show discontiguous harmony, so positional licensing itself must be compatible with both arrangements. SeeKaplan (2018a) for details about how the formalism in (4) accommodates both types of harmony.…”