Domain and codomain of dominance Sample Clauses

Domain and codomain of dominance. ‌ In the next two sections, I briefly discuss heterogeneity with respect to dominance and precedence. Of the other two relations in the model, only dominance is heterogeneous. As in the case of φ-Correspondence, dominance is established between pairs of properties that define the domain and the codomain of the relation. Such pairs (excluding the transitively derived ones15) are {⟨ω, F⟩, ⟨F, σ⟩, ⟨σ, ⊙⟩, ⟨⊙, φ⟩}, which resembles but never overlaps with correspondence pairs {⟨I, O⟩, ⟨B, R⟩, ⟨φH, φ⟩, …}. The pair of domain sets that dominance acts on varies across interpretable elements. An input node cannot dominate an output node, and a head element cannot dominate a non-head element with the same interpretable property. A hierarchy is instead established among interpretable properties. Crucially, the relation is established only among elements with different interpretable properties (i.e., I adopt the Strict Layering Hypothesis, Selkirk 1984: 24). Feet dominate syllables, they do not dominate other feet; root nodes dominate feature nodes, not other root nodes.16 Consider the dominance relation ↓F-σ between feet and syllables. We have: X = {x | x ∈ F ∧ x ∈ O} Y = {x | x ∈ σ ∧ x ∈ O} Like the correspondence example, Axiom I prevents an element from having two or more interpretable features, and X and Y never overlap because F ∩ σ = ∅. The same is true for all the pairs in the domain/codomain set, which makes dominance heterogeneous.