Table Of ContentELIZABETH BOGAL-ALLBRITTEN LSA 2009, SAN FRANCISCO
SWARTHMORE COLLEGE JANUARY 10, 2009
Navajo Degree Constructions and the Decompositional Analysis of
Gradable Predicates1
Outline:
I. Demonstrate that two derivational prefixes marking Navajo gradable predicates are (a) degree
morphemes and (b) determine the semantic type of gradable predicate: ⟨d,et⟩ or ⟨et⟩.
II. Sketch a decompositional approach to Navajo gradable predicates.
III. Discuss how this view of degree morphology is precedented in previous, alternate analyses.
Definitions and assumptions:
• gradable predicates denote properties that hold to a greater or lesser extent for a given object
• degrees adopted as semantic type ⟨d⟩
• degree constructions are morphosyntactic constructions that refer to a degree of gradability and
contain a degree morpheme.
Sally is taller than Anna. Topic of comparison = Sally Standard of comparison = Anna
Gradable predicate = tall Degree morpheme = -er Standard marker = than
1: The Relational Analysis
• Relational analysis (Cresswell 1976; von Stechow 1984; Heim 1985, 2000; Bierwisch 1989; Klein
1991; Kennedy & McNally 2005, inter alia).
o Gradable predicates of type ⟨d,et⟩ and formed from 3 components: a measure function (δ ),
tall
a degree argument (d), and an ordering relation (>).
(1) a. tall (x)(d) = λdλx.δ (x) > d b. Sally is d-tall
⟨d,et⟩ tall
• The degree argument d can be valued in three different ways:
I. Measure phrase: direct saturation of d
II. Degree morpheme: restricts value of d {more/er, less, as, most/est, how, very}
[[more/er]] = d > degree contributed by standard of comparison
III. Positive morpheme: d > contextual standard of comparison; evaluativity
1 The Navajo data in this presentation are from the 1987 edition of the Young and Morgan Navajo dictionary (henceforth YM) and
from fieldwork at the 2008 Navajo Language Academy in Albuquerque, NM. I am grateful to Ellavina Perkins and Irene Silentman
for their insight and assistance: all unattributed examples and grammaticality judgments are due to them. Many thanks are also due to
Theodore Fernald, Christopher Kennedy, and Keren Rice. This work is adapted from Bogal-Allbritten (2008).
The following abbreviations will be used in the glosses: EVID = evidential marker; TOPIC = topic marker; BEYOND = postposition -lááh
‘beyond’; SHORT OF = postposition -'oh ‘short of’; AT = locative enclitic -gi ‘at’; SUB = subordinator/complementizer -go; COMP =
complementizer/nominalizers -í and -ígíí; QPRT = question particle (-sh, lá, sh™’); WH = wh-word; 1,2,3,3’ = person ; sg, dpl, pl =
number; 1sg-, 2sg-, etc. = possessor (‘my’ ‘yours’, etc.).
1
2: Morphosyntax of Navajo degree constructions
• Relevant Navajo morphology and syntax
o Verb stem at far right carries basic meaning of verb. Verb template describes morpheme
ordering: subject, mode/aspect markers, and object inflection in fixed order (right to left)
o SOV word order. Verb-external subject and object DPs are adjuncts (Willie & Jelinek 2000)
• Degree expressions in TABLE A are used in degree constructions.
o Locative/directional adpositions introduce degree relations by marking standard of comparison
(Stassen 1985)
TABLE A Degree expressions2
Navajo Translation Interpretation Type
a. P-lááh ‘beyond P’ X is more A than P (comparative) PP
b. P-‘oh ‘short of P’ X is less A than P (comparative) PP
c. P-ee ‘with P’ X is as A as P (equative) PP
d. DP-gi ‘at DP’ X is as A as P (equative) Enc
e. Haa ‘how, why’ How A is X? (Wh-word) Wh
f. measure phrase MP X is MP A (e.g., X is 6ft tall) DP
g.‘ayóo ‘very’ X is very A (intensifier) Adv
(2) a. Shí sh¶naa¶ bil¡¡h '¡n¶shd¶¶l
1sg. 1sg-older.brother 3sgO-BEYOND ‘á-ní-2-1sgS-big
‘I'm larger than my older brother.’ (YM 1987: d85)
b. Shí shichidí nih-ígíí bilááh ‘át’éego nizhóní
1sg. 1sg-car 2sg-COMP 3sgO-BEYOND 3sgS-be-SUB ni-6-3sgS-pretty
‘My car is prettier than yours.’
3: Focus on alternation between ‘á-ní-2 and ni-6
• ní-2 and ni-6 occupy the position in the verb template associated with mode/aspect markers. ‘á- is a
derivational prefix that always accompanies ní-2 (except in the wh-construction).
• Class I and Class II predicates3
Class I: can be marked with either ni-6 or ‘á-ní-2. Almost exclusively dimension-denoting. A limited
number of predicates with non-dimensional meanings included in Class I.
Class II: can only be marked with ni-6. Predicates with non-dimensional meaning with the addition of
diminutive predicates.
2 P = pronominal inflection; A = adjectival verb; NP = noun phrase; X = any subject; MP = measure phrase
3 YM (1987) refers to Class I predicates as ‘Dimensional adjectivals’ and Class II predicates as ‘Descriptive adjectivals.’
2
TABLE B TABLE C
List of Class I Predicates Selection of Class II Predicates4 .
Translation ni-6 ‘á-ní-2 . T r a n s l ation First person Third person
large, big, tall nitsaa ‘ání¬tso stinky nishchxon nichxon
wide, thick nitsaaz ‘ání¬tsááz white ¬inishgai ¬igai
number nit’é ‘ánílt’e’ round, plump dinishjool dijool
tall nineez ‘ání¬nééz hairy dinish’il di’il
wide niteel ‘ání¬téél wet dinisht¬éé’ dit¬éé’
heavy nidaaz ‘ání¬dáás fast dinishwo’ dilwo’
big - - - ‘áníldííl lightweight ‘ánísts’óózí ‘á¬ts’óózí
big around nimaal ‘ánílmáál small ‘áníst’ísí ‘á¬ts’ísí
pretty nizhóní ‘ánóoshóní
strong bidziil ‘ábóodziil
fast dilwo’ ? ‘ádóolwo’
• YM (1987): semantic distinction based on alternation of ni-6‘and á-ní-2 on Class I predicates.
ni-6+1sgS+neez nisneez ‘I am long or tall in an absolute sense’
‘á-ní-2+1sgS+neez ‘ánísnééz ‘I am long or tall (in a relative or comparative sense)’
(adapt. YM 1987: d117)
• Only the first interpretation is available for Class II predicates.
Informal proposal
ni-6-marked predicates are type ⟨et⟩, positive-marked expressions
‘á-ní-2-marked predicates are type ⟨d,et⟩ expressions
If this is correct, we predict the following differences:
ni-6-marked predicates should: ‘á-ní-2-marked predicates should:
- Not occur in degree constructions requiring a degree - Freely occur in degree constructions that require
argument degree arguments
- Be evaluative, or contribute an evaluative reading to a - Not be obligatorily evaluative
degree construction - Behave syntactically like unsaturated predicates
- Behave like fully saturated predicates with subject even with subject
4: Testing for differences between ‘á-ní-2 and ni-6
4.1: Degree constructions requiring an open degree argument
4 ni-6 disappears in the presence of certain additional derivational prefixes (¬i, ‘á-, and di-) when inflected for third person, but remains
in first person forms. When ni-6 comes between ‘á- and first person inflection, ni-6 is realized with high tone.
3
Measure phrases
Standard view: Degree-denoting measure phrase directly saturates the degree argument.
tall (Sally)(5ft) = 1 iff δ (Sally) > 5ft
⟨d,et⟩ tall
⇒ Only ‘á-ní-2-marked predicates can take measure phrase. Any dimension-denoting ‘á-ní-2-marked
predicate can take a measure phrase.
• ni-6-marked predicates never take a measure phrase, even if they denote a dimension.
(3) a. Tseebíí dahidídlo’ ‘ání¬dáás / *nidaaz
eight pound ‘á-ní-2-3sgS-heavy ni-6-3sgS-heavy
‘It weighs eight pounds.’
b. K¡¡'ts'¶n¶ n¡h¡st'¢¶ dºº n¡¡'¡¬n¶i'j•' k¢ sil¡a-gi '¡n¶¬n¢¢z / * nineez
alligator nine and half-LOC foot-AT ‘á-ní-2-3sgS-tall ni-6-3sgS-long
‘The alligator is nine and a half feet long.’ (adapt. YM 1987: d492)
c. Dízdiin dah alzhin ‘¡n¶shm¡¡l / *nismaal
four inch ‘á-ní-2-1sgS-big.around ni-6-1sgS-big.around
‘I am forty inches around.’
Comparative subdeletion construction
Standard view: Degree arguments of two predicates compared with degree morphology.
a. The table is higher than the door is wide.
b. [[more/er]] = λd.λd’.max(d’) > max(d) (Vanderelest 2008)
c. max(λd’.the table is d’-high) > max(λd.the door is d-wide)
⇒ ‘á-ní-2-marked predicates can be used in comparative subdeletion constructions5
(4) a. Díí naaltsoos ‘ání¬téél-ígíí yilááh ‘ání¬nééz
DET book ‘á-ní-2-3sgS-wide-COMP 3sg’O-BEYOND ‘á-ní-2-3sgS-long
‘This book is longer than it is wide.’
b. Ch’é’étiin bikáá’adání ‘ání¬nééz-í-gi ‘ání¬téél
doorway table ‘á-ní-2-3sgS-long-COMP-AT ‘á-ní-2-3sgS-wide
‘The doorway is as wide as the table is long.’
⇒ Use of ni-6-marked predicate in either matrix or in comparative site judged ungrammatical
5 In comparative subdeletion construction, the complementizer –ígíí marks the predicate functioning as the standard of comparison.
4
(5) a. *Díí naaltsoos niteel-ígíí yilááh ‘ání¬nééz
DET book ni-6-3sgS-wide-COMP 3sg’O-BEYOND ‘á-ní-2-3sgS-long
(‘This book is longer than it is wide.’)
b.?*Díí naaltsoos ‘ání¬téél-ígíí yilááh ‘át’éego nineez
DET book ‘á-ní-2-3sgS-wide-COMP 3sg’O-BEYOND 3sgS-be-SUB ni-6-3sgS-long
(‘This book is longer than it is wide.’)6
4.2: Differences in semantics of degree constructions
Equative construction
Standard view: Degree morpheme as semantically restricts the value of the degree argument of matrix
predicate to equal the degree contributed by the standard of comparison.
⇒ ‘á-ní-2-marked predicates: ‘exact non-evaluative’ reading
(6) a. Ni-gi ‘ánísnééz
2sg-AT ‘á-ní-2-1sgS-tall
‘I am as tall as you.’
b. Hastiin Yazhí be’esdzáán chªªh yee ‘adilohii-gi ‘ání¬dáás
Mr. Yazhí 3sg-wife elephant-AT ‘á-ní-2-3sgS-heavy
‘Mr. Yazhí’s wife is as heavy as an elephant.’ (YM 1987: g192)
⇒ ni-6-marked predicates: ‘inexact but evaluative’ reading
(7) a. Ni-gi ‘át’éego nisneez
2sg-AT 3sgS-be-SUB ni-6-1sgS-tall
‘I am tall like you.’ (YM 1987: g193)
b. Bínaaí ‘át’éhé-gi ‘át’éego dilwo’
3sg-older.brother-AT 3sgS-be-SUB ni-6-3sgS-fast
‘He’s a fast runner just like his older brother.’ (YM 1987: d369)
Intensifier construction
Standard view: Intensifier takes contextual standard of comparison and raises it (see Klein 1980,
Kennedy and McNally 2005 for two variations)
⇒ ‘ayóo obligatorily contributes a high-degree reading when it modifies ni-6-marked predicates,
typically contributes a high-degree reading with ‘á-ní-2-marked predicates.
6 Note the obligatory presence of ‘át’éego between nineez and yilááh in (7b) and (2b). ‘át’éego is composed of a copular verb (‘át’é)
marked with the subordinator/adverbializer –go. It obligatorily appears in degree constructions (except with ‘ayóo) when a ni-6-
marked predicate is used. The semantic and syntactic contribution of ‘át’éego is discussed at length in Bogal-Allbritten (2008).
5
(8) a. N¡st¡¡n ¬a' dz¶dzaasht••h `t'¢¢' 'ayºo nidaaz l¡
log DET 1sgS-put.slender.object.in.fire PAST very ni-6-3sgS-heavy EVID
‘I was going to put a log into the fire but it was too heavy.’ (adapt. YM 1987: d358)
b. ~l¢¶ hastiin bizoo¬ dah dijool¶g¶¶ 'ayºo '¡n¶¬tsxo
DET man 3sg-windpipe 3sgS-round-COMP very ‘á-ní-2-3sgS-large
‘That man has a huge Adam's Apple.’ (YM 1987: d144)
⇒ ‘áyóo can also contribute a positive-degree reading with ‘á-ní-2-marked predicates.
(9) a. Sh¶naa¶ 'ayºo '¡n¶¬d¡¡s, sh¶ '¢¶ '¡n¶szºl¶
1sg.older.brother very ‘á-ní-2-3sgS-heavy 1sg. TOPIC ni-6-1sgS-light
‘My big brother is heavy, (but) I'm light in weight.’ (YM 1987: d117)
NOT very heavy
b. Dib¢ y¡zh¶ ¬a' bin¡¡haigo 'ayºo '¡n¶ld¶íl ¬eh
sheep small DET one-winter.pass-SUB very ‘á-ní-2-3sgS-big usually
‘A lamb is usually big when it is a year old.’ (YM 1987: d116)
NOT very big
⇒ Mandarin hen ‘very’ also contributes a positive-degree reading (Sybesma 1999, Grano 2008)
4.3: Obligatory presence of the degree expression
• ‘á-ní-2-marked predicates are ungrammatical if not directly preceded by a degree expression.
o This restriction holds even in a suitable discourse context, c.f. (9a).
• ni-6-marked predicates are grammatical in the absence of a degree expression
(10) a. *‘ádóoshwo’ b. dinishwo’
‘á-ní-2-1sgS-fast ni-6-3sgS-fast
(‘I am fast in a relative or comparative sense’) ‘I am fast.’
(11) a. *’ánóoshóní b. nizhóní
‘á-ní-2-3sgS-pretty ni-6-3sgS-pretty
(‘S/he is attractive in a relative or comparative sense’) ‘S/he is attractive.’
• ‘á-ní-2-marked predicates must saturate a degree argument position, while ni-6-marked predicates are
only setting a contextual standard
6
5: Analysis: ‘á-ní-2 and ni-6 are degree morphemes
ni-6-marked predicates: ‘á-ní-2-marked predicates:
Do not occur in degree constructions requiring a Freely occur in degree constructions that require
degree argument degree arguments
Are evaluative, or contribute an evaluative reading to a Are not obligatorily evaluative
degree construction Behave like unsaturated predicates
Behave like fully saturated predicates
⇒ Relational analysis is untenable for Navajo
I. Decompositional analysis (Kennedy 1997)
o Gradable predicates reduced to measure functions of type ⟨ed⟩, e.g. δ (x)
tall
o Three roles performed by degree morphemes (e.g., pos, more, less, as, meas)
1. introduce ordering relation
2. convert measure function into property of individuals
3. determine presence or absence of an open degree argument
Formalizing the distinction
[[ni-6]] = λsλx.s(x) > STND(s) Positive morpheme
[[‘á-ní-2]] = λsλdλx.s(x) > d Generalized degree morpheme
(s is a verb stem (measure function, type ⟨ed⟩), x is an individual of type ⟨e⟩, d is a degree of type ⟨d⟩)
• Focusing on functions 2 and 3 of degree morphology: all degree morphemes can be placed in two
broad categories: pos vs. everything else
1.) After composition of the measure function with pos, the meaning of the predicate is complete.
[[ pos]] = λs λx.s(x) > STND(s) (adapt. Kennedy 2007b, In press)
DEG ⟨ed⟩
2.) After composition of the measure function with all other degree morphemes, something else (a
standard of comparison, a measure phrase, etc.) is still required.
[[ more/er]] =λsλdλx.max(s)(x) ≻ d (adapt. Kennedy 2007a,b)
DEG
[[ meas]] = λsλdλx.s(x) > d (adapt. Svenonius & Kennedy 2006)
DEG
(s is a measure function of type ⟨ed⟩, x is an individual of type ⟨e⟩, d is a degree of type ⟨d⟩)
• Navajo degree morphology reflects this split by differentiating between ni-6 and ‘á-ní-2
II. How does the analysis of Navajo fit into the cross-linguistic picture?
⇒ Shifting the semantics of comparison to the standard marker (Kennedy 2007a). Standard
marker determines type of standard of comparison (phrasal vs. clausal) and introduces
ordering relation.
7
Greek exhibits morphological comparatives (Bobaljik 2007: 53).
⇒ apo to mark phrasal standards of comparisons and apoti to mark clausal standards of
comparison (Merchant 2006).
Revised view (Kennedy 2007a: 7)
[[ apo]] = λyλgλx.max(g)(x) > max(g)(y) phrasal
STND
[[ apoti]] = λdλgλx.max(g)(x) > d clausal
STND
(g is a gradable predicate of type ⟨d,et⟩ , x and y are an individuals of type ⟨e⟩, d is a degree of type ⟨d⟩)
⇒ This leaves degree morphology meaningless unless we assume gradable predicates are not
type ⟨d,et⟩ expressions. Two options:
• type ⟨ed⟩ (measure functions) or
• type ⟨et⟩ (properties of individuals)
⇒ The task of degree morphology is to convert the gradable predicate into a degree relation of
type ⟨d,et⟩ …which is precisely my proposal for ‘á-ní-2 in Navajo
6: Conclusions
• A decompositional analysis best accounts for the semantics of Navajo gradable predicates.
Alternation in semantic type of gradable predicates is determined by alternation in ni-6 and ‘á-ní-2.
o Composition of a verb stem with ni-6 produces a type ⟨et⟩ expression.
o Composition of a verb stem with ‘á-ní-2 produces a type ⟨d,et⟩ expression.
• This alternate view of degree morphology has precedent in a reduced form of the decompositional
analysis and a more recent proposal for a revised view of the degree morphology vs. standard marker
relation.
7: Appendix
Wh-construction [Not discussed in this presentation]
Standard view: Degree operator binds degree argument.
a. How tall is John?
b. OPd[d = max(λd’[John is d’-tall])]
c. What is the maximal degree d such that John is d-tall? (adapt. Rullmann 1995: 136)
⇒ ní-2-marked predicates: degree reading obligatory, predicate not assigned evaluative
interpretation.
(12) Haa ní¬tso?
WH ní-2-3sgS-large
‘How large is it?’ or ‘What size is it?’ Degree reading
8
⇒ ni-6-marked predicates: descriptive reading preferred, evaluative reading of predicate
presupposed.
(13) Haash yit’éego ‘á¬ts’óózí
WH-QPRT 3sgS-be-SUB ni-6-3sgS-thin
‘Why is s/he skinny?’ or ‘How is it that s/he is skinny?’ Descriptive reading
?? ‘How skinny is s/he?’ Degree reading
8: Works Cited
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