## Background to degree and comparative constructions

- Dimension adjectives
- Degree constructions
  - Modification of modifiers
  - Measure modification
  - Dimension noun
- Comparative constructions

### Dimension adjectives

As is well known, certain adjectives are gradable; that is, the properties referred to by the adjectives characterize entities that can exhibit those properties to a greater or lesser extent or degree. In what follows, we refer to the gradable properties as dimensions and to the adjectives expressing them as dimension adjectives. Dimension adjectives can be modified, with the resulting expression corresponding to some point on a scale. The scale represents the dimension, and the modifier specifies the point.

>     ( (ADJP (ADV barely / hardly / unusually / unexpectedly / very)
>     	(ADJ warm)))

Note: The following discussion focuses on adjectives, but extends in a straightforward way to gradable adverbs.

### Degree constructions

The degree to which an entity exhibits a dimension may be correlated with some other property. In particular, the correlating property might hold beyond (above or below) a certain threshold point for its dimension. This type of correlation is highlighted by a type of modifier that we will call a degree head; we will refer to the phrase expressing the correlating property as the degree complement. Our annotation treats degree heads as heads of modifiers on a par with other modifiers of dimension adjectives. They are tagged as ordinary adverbs (`ADV`) if they end in -ly and as comparative adverbs (`ADVR`) otherwise; in both cases, they project `ADVP` if necessary. Even though the degree complement depends on the degree head (not on the dimension adjective), the annotation represents all three expressions as sisters.

>     ( (ADJP (ADV overly / sufficiently)   	        ← degree head
>     	(ADJ warm)				← dimension adjective
>     	(PP (P for)				← degree complement
>     	    (NP (N comfort)))))

>     ( (ADJP (ADVR so)
>     	(ADJ warm)
>     	(CP-DEG (C that / 0)
>     		(IP-SUB (NP-SBJ (PRO we))
>     			(BED were)
>     			(ADJP-PRD (ADJ uncomfortable))))))

>     ( (ADJP (ADVR too)
>     	(ADJ hot)
>     	(PP (P for)
>     	    (NP (N comfort)))))

>     ( (ADJP (ADVR too)
>     	(ADJ hot)
>     	(IP-INF-DEG (TO to)
>     		    (BE be)
>     		    (ADJP-PRD (ADJ comfortable)))))

>     ( (ADJP (ADVR too)
>     	(ADJ hot)
>     	(IP-INF-DEG (FOR for)
>     		    (NP-SBJ (PRO us))
>     		    (TO to)
>     		    (BE be)
>     		    (ADJP-PRD (ADJ comfortable)))))

>     ( (ADJP (ADVR too)
>     	(ADJ hot)
>     	(CP-EOP (WNP-1 0)
>     		(IP-INF (NP-OB1 *T*-1)
>     			(TO to)
>     			(VB drink)))))

The degree complement may be absent in the syntax.

>     ( (ADJP (ADV overly / sufficiently)		← degree head
>     	(ADJ warm)))				← dimension adjective

>     ( (IP-MAT (NP-SBJ (PRO It@))
>     	  (BEP @'s)
>     	  (ADJP-PRD (ADVR so)			← degree head
>     		    (ADJ warm))			← dimension adjective
>     	  (PUNC .)))

In connection with the degree head SO, the dimension adjective can be absent in the syntax. In these cases, SO is tagged as `P` rather than `ADVR`. See SO AS (THAT), SO AS TO for examples and SO (THAT) for related discussion.

#### Modification of modifiers

Degree modifiers may themselves may be modified. By convention, extraposition from positions not available in the surface syntax is not annotated.

>     ( (ADJP (ADVP (Q all) (ADVR too))
>     	(ADJ hot)))

>     ( (ADJP (ADVP (QP (ADV very) (Q much))
>     	      (ADVR too))
>     	(ADJ hot)))

>     ( (ADJP (ADVP (ADV barely) (ADV sufficiently))
>     	(ADJ hot)))

>     ( (NP (ADJP (ADV barely)
>     	    (ADJR enough))))

>     ( (ADJP (ADV barely)
>     	(ADJ hot)
>     	(ADVP (ADVR enough))))		← like this

>     ( (ADJP (ADVP (ADV barely)
>     	      (ADVP *ICH*-1))
>     	(ADJ hot)
>     	(ADVP-1 (ADVR enough))))	← not like this

>     ( (ADJP (ADV-1 barely)
>     	(ADJ hot)
>     	(ADVP (ADV *ICH-1)
>     	      (ADVR enough))))		← not like this

#### Measure modification

So far, we have discussed qualitative degree modifiers. A subset of dimension adjectives, given below, additionally allows quantitative, or measure, modification.

>     Spatial:   DEEP, DISTANT, FAR, HIGH, LONG, TALL, WIDE

>     Temporal:  EARLY, LATE, OLD

>     Other:     WORTH

This type of modification corresponds to the everyday procedure of measuring some length using a ruler. The extent to which an entity exhibits the dimension under discussion is defined in terms of an interval bounded by two endpoints associated with the entity. The interval is mapped onto an interval on the scale associated with the dimension (the ruler). The scale in question has properties that go beyond scales associated with qualitative modification. In particular, it has an origin or zero point, and it is divided into equal units. In other words, the scale is isomorphic to the natural numbers. The zero point on the scale is aligned with one of the endpoints on the entity, and the point on the scale corresponding to the other endpoint on the entity yields a numerical measure of the degree to which the entity exhibits the dimension. The following expressions spell out the various parameters just introduced, apart from the zero point on the scale, which is constant and hence never expressed.

>     ( (ADJP (NP-MSR (NUM three)			← second endpoint on scale
>     		(NS feet))			← unit of measurement
>     	(ADJ wide)				← dimension adjective
>     	(PP (P from)
>     	    (NP (D the)				← first endpoint on entity
>     		(ADJ left)
>     		(N edge)))
>     	(PP (P to)
>     	    (NP (D the)				← second endpoint on entity
>     		(ADJ right)))))

>     ( (ADJP (NP-MSR (NUM three)			← second endpoint on scale
>     		(NS years))			← unit of measurement
>     		(ADJ old)			← dimension adjective
>     		(PP (P from)
>     		    (NP (N birth)))		← first endpoint on entity
>     		(PP (P to)
>     		    (NP (D the)			← second endpoint on entity
>     			(ADJ present)
>     			(N moment))))))

The interval between the endpoints can be further described (say, in terms of its properties as a path).

>     ( (ADJP (NP-MSR (NUM twenty)			← second endpoint on scale
>     		(NS miles))			← unit of measurement
>     	(ADJ distant)				← dimension adjective
>     	(PP (P from)
>     	    (NP (D the)				← first endpoint on entity
>     		(N center)
>     		(PP (P of)
>     		    (NP (N town)))))
>     	(PP (P to)
>     	    (ADVP (ADV here)))			← second endpoint on entity
>     	(PP (P by)				← path descriptor
>     	    (NP (ADJ winding)
>     		(NS roads)))))

>     ( (ADJP (NP-MSR (NUM thirty-six)		← second endpoint on scale
>     		(NS inches))			← unit of measurement
>     	(ADJ long)				← dimension
>     	(PP (P in)				← path descriptor
>     	    (NP (N circumference)))))

In ordinary usage, various parameters, including the dimension itself, are often not overtly expressed. In order to clarify the structure, silent heads of measure phrases and silent dimension adjectives may be added to the annotation. Implicit endpoints on the entity are not annotated, however.

>     ( (ADJP (NP-MSR (NUM three)
>     		(NS feet))
>     	(ADJ 0)				← implicit dimension (WIDE)
>     	(PP (P from)			← implicit second endpoint on entity
>     	    (NP (D the)
>     		(ADJ left)
>     		(N edge)))

>     ( (ADJP (NP-MSR (NUM three)
>     		(NS feet))
>     	(ADJ 0)				← implicit dimension (HIGH)
>     	(PP (P to)			← implicit first endpoint on entity
>     	    (NP (D the)
>     		(N top)))))

>     ( (ADJP (NP-MSR (NUM three)
>     		(NS years))
>     	(ADJ old)			← implicit first and second endpoints

>     ( (ADJP (NP-MSR (NUM three)
>     		(NS months))
>     	(ADJ 0)				← implicit dimension (OLD)

>     ( (IP-MAT (NP-SBJ (PRO She))
>     	  (ADVP-TMP (ADV just))
>     	  (VBD turned)
>               (ADJP-PRD (NP-MSR (NUM three)
>        			    (NS 0))	← implicit unit (YEARS)
>     		    (ADJ 0)))		← implicit dimension (OLD)
>     	  (PUNC .)))

#### Dimension noun

Dimensions can also be expressed by nominal heads. In such cases, the entire construction is annotated as a noun phrase, with a dash tag appropriate to the syntactic context. The syntactic head of the entire NP construction is not usually the dimension noun.

>     ( (NP (NUM thirty-six)
>           (NS years)		← head of NP =/= dimension head
>           (PP (P of)
>     	  (NP (N age)))))	← dimension (OLD) expressed, but not as ADJ

>     ( (PP (P from)
>           (NP (NUM thirty-six)
>     	  (NS years)
>     	  (PP (P of)
>     	      (NP (N age))))))

>     ( (IP-MAT (NP-SBJ (PRO It))
>     	  (BEP is)
>               (NP-PRD (NUM thirty-six)
>         	          (NS inches)			← head of NP =/= dimension head
>     	          (PP (P in)
>     	     	      (NP (N length))))		← dimension (LONG) expressed, but not as ADJ
>     	  (PUNC .)))

The integration of scalar constructions into larger constituents follows general principles.

>     ( (NP (D a)
>           (N child)
>           (ADJP (NP-MSR (NUM eight)			← postnominal ADJP
>     	    	    (NS years))
>     	    (ADJ old)))))			← head of dimension construction = ADJ

>     ( (NP (D a)
>           (N child)
>           (PP (P of)				← postnominal PP
>     	  (ADJP (NP-MSR (NUM eight)
>     	                (NS years))
>                     (ADJ old)))))			← head of dimension construction = ADJ

>     ( (NP (D a)
>           (N child)
>           (PP (P of)
>               (ADJP (NP-MSR (NUM eight)
>     			(NS 0))
>     		(ADJ 0)))))

>     ( (NP (D a)
>           (N child)
>           (RRC (NP-PRD (NUM eight)			← postnominal NP
>               	   (NS years) 			← head of dimension construction = NS
>     		   (PP (P of)
>     		       (NP (N age)))))))

### Comparative constructions

Comparative constructions are similar to degree constructions. Instead of a pure degree head associated with a degree complement, they contain a comparative degree head associated with a standard of comparison. Comparative clauses (`CP-CMP`) are Wh- CP. The wh- antecedent is silent; its syntactic category is generally the wh- phrase counterpart to the syntactic category of the dimension of comparison (but see below for comparative subdeletion).

>     ( (ADJP (QR more)				← degree head
>     	(ADJ dangerous)				← dimension of comparison
>             (CP-CMP (WADJP-1 0)			← complement of degree head
>                     (C than)
>                     (IP-SUB (ADJP-PRD *T*-1)
>                             (NP-SBJ (D a) (N rattlesnake))
>     		        (BEP is)))))

>     ( (NP (QP (ADVR as) 				← degree head
>               (Q many) 				← dimension of comparison
>           (NS cookies)
>           (CP-CMP (WNP-1 0)				← complement of degree head
>                   (C as)
>                   (IP-SUB (NP-OB1 *T*-1)
>                           (NP-SBJ (PRO you))
>     		      (VBD baked)))))

In synthetic comparatives, the degree head and the dimension of comparison are expressed in a single word.

>     ( (ADJP (ADJR taller)				← degree head + dimension of comparison
>     	(CP-CMP (WADJP-1 0)			← complement of degree head
>     		(C than)
>                     (IP-SUB (ADJP-PRD *T*-1)
>                             (NP-SBJ (PRO you))
>                             (BEP are)))))

>     ( (ADVP (ADVR faster)				← degree head + dimension of comparison
>     	(CP-CMP (WADVP-1 0)			← complement of degree head
>     		(C than)
>                     (IP-SUB (ADVP *T*-1)
>                             (NP-SBJ (PRO they))
>     			(MD could)
>     			(VB run)))))

>     ( (NP (QR more)					← degree head + dimension of comparison
>           (NS cookies)
>           (CP-CMP (WNP-1 (WPRO 0))			← complement of degree head
>     	      (C than)
>                   (IP-SUB (NP-OB1 *T*-1)
>                           (NP-SBJ (PRO you))
>     		      (VBD baked))))

As with degree constructions, the complement of the comparative degree head can be silent in the syntax.

>     ( (NP (QR more) (NS cookies)

>     ( (ADJP (QR more) (ADJ important)))

>     ( (ADVP (ADVR faster)))

As expected, the degree head can be modified. Any modifiers of AS are generally not set off with AS as a pharse.

>     ( (ADJP (QP (Q much) (QR more))
>     	(ADJ dangerous)))

>     ( (ADJP (QP (NP-MSR (Q many) (NS times))
>     	    (QR more))
>     	(ADJ dangerous)))

>     ( (ADJP (ADV equally)                        ← no ADVP around EQUALLY AS
>             (ADVR as)
>     	(ADJ important)))

Comparative structures may themselves function as modifiers.

>     ( (ADVP-LOC (NP-MSR (ADJR further))
>     	    (ADV away)
>     	    (PP (P from)
>     		(NP (D the)
>     		    (N house)))))

>     ( (ADVP-LOC (NP-MSR (ADJP (FP even)
>     			  (ADJR further)))
>     	    (ADV away)
>     	    (PP (P from)
>     		(NP (D the)
>     		    (N house)))))

>     ( (ADVP-LOC (NP-MSR (ADJP (NP-MSR (NUMP (NUM five))
>     				  (NS miles))
>     			  (ADJR further)))
>     	    (ADV away)
>     	    (PP (P from)
>     		(NP (D the)
>     		    (N house)))))

>     ( (NP (ADJP (QP (NP-MSR (NUMP (NUM five))
>     			(NS times))
>     		(QR more))
>     	    (ADJ serious))
>           (NS problems)
>           (CP-CMP (WNP-1 (WPRO 0))
>     	      (IP-SUB (NP-OB1 *T*-1)
>     		      (NP-SBJ (PRO they))
>     		      (HVD had)
>     		      (ADVP-TMP (ADV ever))
>     		      (VBN encountered)))))