What seems to be at work here is the requirement that the two outputs of
Search 0 , Σ and λ, be minimally distant. In order to formulate this requirement,
let us introduce the notion of “Structural Prominence” as a measure for struc-
tural distance:
(31) Structural Prominence (see Narita and Fukui 2016; see also Ohta et al.
2013 for a related notion of “Degree of Merger”):^23
Suppose that Depth(α) = m (m ≥ 0) is the order of depth – the inverse
relation of prominence – associated with an SO α, with lower prominence
indicated by a higher value of depth. Then, we can say:
a. Depth(α) = 0 if there is no SO β such that α ∈ β (i.e., α is a root SO
dominated by no other SO).
b. If Depth(α) = m, then Depth(β) = m + 1 for any β such that β ∈ α
(i.e., β is a daughter of α).
(31a) states that “undominated” SOs are the most prominent in WS. (31b)
states that the value of Depth(α) increases as α gets more deeply embedded
and less prominent. In (29), for example, Depth(vP) = 0, Depth(v) = 1,
Depth(read) = 2, Depth(n) = 3, etc. As shown in (30), v but not read or n is
a legitimate output of Search 0 in service of labeling, given that v is the most
prominent lexical element that can defi ne a label for some SO.
Capitalizing on (31), we can formulate a minimality condition on M 0 ◦S 0 as
in (32), which basically serves to minimize the distance between the two outputs
of Search 0.
(32) Minimality Condition on M 0 ◦S 0 :
For any linguistic relation R, M 0 ◦S 0 (WS) may generate {α, β} as an instance
of R only if
a. {α, β} meets formal restrictions on R, and
b. There is no γ such that {α, γ} also meets the formal restrictions on R,
and Depth(γ) < Depth(β).
(32) essentially recaptures the intuition of Rizzi’s (1990) “Relativized Minimal-
ity” in the theory of M 0 ◦S 0. It holds that a relation between α and β cannot
be established if there is any intervening element γ that can formally participate
in R with α and is “closer” to α than β. Specifi cally for the Label(ing)-relation,
we propose (33) as its formal restriction.
(33) Label:
{α, β} may count as an instance of Label only if
a.α is a (bundle of ) feature(s) (typically an LI),^24 and
b.α is contained in β.Given the formal restriction in (33), the minimality condition in (32) can
explain cases like (30): Search 0 (WS) can access any of vP, v, read, n, etc. in
38 Takaomi Kato et al.