Its sometimes suggested that stringency systems are a

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It’s sometimes suggested that stringency systems are a better idea because they avoid the need to stipulate a fixed ranking. But both approaches require some sort of stipulation, fixed ranking in one approach and continuous ranges anchored at one end of scale in the other. A more substantial difference is that stringency systems predict a wider variety of possible languages than do fixed hierarchies, keeping all else equal.
4.5.3 Constraints derived by harmonic alignment: 39 Example: The issue in this invented language is how to syllabify an input like /pmr/ as a single syllable without epenthesis or deletion. Should it be with syllabic and a complex onset or with syllabic and a simple onset? This is a choice between ’s better nucleus and ’s simple onset.
4.5.3 Constraints derived by harmonic alignment: 40 The language tolerates a complex onset if the alternative requires a syllable nucleus with sonority lower than that of a liquid. (a-c) The sonority advantage of a fricative nucleus over a stop nucleus won’t override *Complex-Onset. (e-f)
4.5.3 Constraints derived by harmonic alignment: 41 Analysis:
4.5.3 Constraints derived by harmonic alignment: 42 Result: This is an anti-Paninian hierarchy because the general constraint in a stringency relation, *Nucleus/Plosive–Nasal, dominates the more specific constraints *Nucleus/Plosive–Fricative and *Nucleus/Plosive. Because constraints in a stringency relation are never directly rankable this demonstration necessarily involves transitivity of constraint domination via *Complex-Onset.
4.5.3 Constraints derived by harmonic alignment: 43 Result: Fixed hierarchies and Paninian rankings give the same results, but the fixed hierarchy has no way of reproducing the effect of the anti-Paninian ranking. If real languages work like this, then the formulation of constraints in stringency rather than fixed-ranking form is supported
4.6 Properties of Faithfulness Constraints 4.6.1 Correspondence theory: 44 A faithfulness constraint assigns its violation marks based on disparities between the input and the output. In principle, any input-output difference could elicit a faithfulness violation.
4.6 Properties of Faithfulness Constraints 4.6.1 Correspondence theory: 45 Correspondence theory provides a general framework for defining faithfulness constraints (McCarthy and Prince 1995, 1999). The idea is that each candidate supplied by Gen includes an output representation and a relation between the input and that output. This is called the correspondence relation , and it’s conventionally denoted by . The relation associates some or all of the linguistic elements in the input with some or all of the linguistic elements in the output.
4.6 Properties of Faithfulness Constraints 4.6.1 Correspondence theory: 46 Example: Since it requires preservation of input elements, it quantifies universally over the elements of the input, requiring each of them to have an output correspondent
4.6 Properties of Faithfulness Constraints 4.6.1 Correspondence theory: 47 Example:

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