Adjectival Predicate Lexicon Fragment

Gradable adjective entries following [Ken07], typed with Semantics.Gradability.GradableAdjective (the syntactic Syntax/Adjective lexeme refined with the degree-semantic layer). Each entry stores its surface form, scalar dimension, lexicalized pole (isLowerEndpoint) or standardOverride, and antonym data; the scale shape (scaleType), positive standard, and Kennedy adjectiveClass are derived views, not stored — the fix for the old scaleType field that conflated scale shape with pole (wet/dry share one closed .wetness scale). The derived Kennedy classification is exercised at the end of this file.

@[reducible, inline]

abbrev English.Predicates.Adjectival.AdjectivalPredicateEntry : Type

[Ken07] An adjectival predicate entry.

This is an alias for GradableAdjective from the Theory module, re-exported here for the Fragments organization.

Equations

• English.Predicates.Adjectival.AdjectivalPredicateEntry = Semantics.Gradability.GradableAdjective

def English.Predicates.Adjectival.tall : AdjectivalPredicateEntry

"tall" — open scale, contrary to "short"

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def English.Predicates.Adjectival.short : AdjectivalPredicateEntry

"short" — open scale, contrary to "tall"

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def English.Predicates.Adjectival.happy : AdjectivalPredicateEntry

"happy" — open scale, contrary to "unhappy"

Note: This is the 1-place adjectival predicate "x is happy". For the 2-place attitude predicate "x is happy that p", see Semantics/Attitudes/Preferential.lean.

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def English.Predicates.Adjectival.unhappy : AdjectivalPredicateEntry

"unhappy" — open scale, contrary to "happy"

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def English.Predicates.Adjectival.sad : AdjectivalPredicateEntry

"sad" — open scale, contrary to "happy" (near-synonym of unhappy)

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def English.Predicates.Adjectival.full : AdjectivalPredicateEntry

"full" — closed scale, contradictory to "empty"

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def English.Predicates.Adjectival.empty : AdjectivalPredicateEntry

"empty" — closed fullness scale, lower pole ⇒ minimum standard, contradictory to "full".

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def English.Predicates.Adjectival.hot : AdjectivalPredicateEntry

"hot" — open scale, contrary to "cold"

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def English.Predicates.Adjectival.cold : AdjectivalPredicateEntry

"cold" — open scale, contrary to "hot"

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def English.Predicates.Adjectival.expensive : AdjectivalPredicateEntry

"expensive" — open scale, contrary to "cheap"

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def English.Predicates.Adjectival.cheap : AdjectivalPredicateEntry

"cheap" — open scale, contrary to "expensive"

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def English.Predicates.Adjectival.wet : AdjectivalPredicateEntry

"wet" — closed wetness scale, lower pole ⇒ minimum standard (true with any non-zero wetness). Shares the closed .wetness scale with "dry"; the two differ only in pole.

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def English.Predicates.Adjectival.dry : AdjectivalPredicateEntry

"dry" — closed wetness scale, upper pole ⇒ maximum standard (true only at complete dryness).

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def English.Predicates.Adjectival.clean : AdjectivalPredicateEntry

"clean" — closed scale (maximally clean), contradictory to "dirty"

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def English.Predicates.Adjectival.dirty : AdjectivalPredicateEntry

"dirty" — closed scale (maximally dirty), contradictory to "clean"

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def English.Predicates.Adjectival.straight : AdjectivalPredicateEntry

"straight" — closed scale (maximally straight), contradictory to "bent"

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def English.Predicates.Adjectival.flat : AdjectivalPredicateEntry

"flat" — closed scale (maximally flat), contradictory to "bumpy"

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def English.Predicates.Adjectival.open_ : AdjectivalPredicateEntry

"open" — closed scale (maximally open), contradictory to "closed"

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def English.Predicates.Adjectival.closed_ : AdjectivalPredicateEntry

"closed" — closed scale, contradictory to "open"

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def English.Predicates.Adjectival.shut : AdjectivalPredicateEntry

"shut" — closed scale, contradictory to "open" (near-synonym of "closed")

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def English.Predicates.Adjectival.free_ : AdjectivalPredicateEntry

"free" — closed scale (maximally free = unattached), contradictory to "stuck"

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def English.Predicates.Adjectival.loose : AdjectivalPredicateEntry

"loose" — closed scale (maximally loose), contradictory to "tight"

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def English.Predicates.Adjectival.tight : AdjectivalPredicateEntry

"tight" — closed scale (maximally tight), contradictory to "loose"

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def English.Predicates.Adjectival.bent : AdjectivalPredicateEntry

"bent" — closed straightness scale, lower pole ⇒ minimum standard (true with any non-zero bend). Shares the closed .straightness scale with "straight".

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def English.Predicates.Adjectival.smooth : AdjectivalPredicateEntry

"smooth" — closed scale, contradictory to "rough"

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def English.Predicates.Adjectival.rough : AdjectivalPredicateEntry

"rough" — closed scale, contradictory to "smooth"

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def English.Predicates.Adjectival.hard : AdjectivalPredicateEntry

"hard" — open scale, contrary to "soft"

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def English.Predicates.Adjectival.soft : AdjectivalPredicateEntry

"soft" — open scale, contrary to "hard"

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def English.Predicates.Adjectival.pure_ : AdjectivalPredicateEntry

"pure" — closed scale (maximally pure), contradictory to "impure"

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def English.Predicates.Adjectival.dead : AdjectivalPredicateEntry

"dead" — closed scale (absolute: maximal endpoint), contradictory to "alive"

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def English.Predicates.Adjectival.alive : AdjectivalPredicateEntry

"alive" — closed scale (absolute), contradictory to "dead"

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def English.Predicates.Adjectival.large : AdjectivalPredicateEntry

"large" — open scale, contrary to "small"

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def English.Predicates.Adjectival.small : AdjectivalPredicateEntry

"small" — open scale, contrary to "large"

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def English.Predicates.Adjectival.gigantic : AdjectivalPredicateEntry

"gigantic" — open scale, contrary to "tiny", informationally stronger than "large"

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def English.Predicates.Adjectival.tiny : AdjectivalPredicateEntry

"tiny" — open scale, contrary to "gigantic", informationally stronger than "small"

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def English.Predicates.Adjectival.pristine : AdjectivalPredicateEntry

"pristine" — closed scale, contrary to "filthy" (extreme absolute: gap exists)

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def English.Predicates.Adjectival.filthy : AdjectivalPredicateEntry

"filthy" — closed scale, contrary to "pristine" (extreme absolute: gap exists)

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def English.Predicates.Adjectival.long : AdjectivalPredicateEntry

"long" — open scale, contrary to "short" (length dimension)

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def English.Predicates.Adjectival.wide : AdjectivalPredicateEntry

"wide" — open scale, contrary to "narrow"

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def English.Predicates.Adjectival.cool : AdjectivalPredicateEntry

"cool" — open scale, contrary to "warm"

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def English.Predicates.Adjectival.warm : AdjectivalPredicateEntry

"warm" — open scale, contrary to "cool"

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Physical dimension adjectives

def English.Predicates.Adjectival.heavy : AdjectivalPredicateEntry

"heavy" — open scale, contrary to "light"

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def English.Predicates.Adjectival.light : AdjectivalPredicateEntry

"light" — open scale, contrary to "heavy"

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def English.Predicates.Adjectival.thick : AdjectivalPredicateEntry

"thick" — open scale, contrary to "thin"

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def English.Predicates.Adjectival.thin : AdjectivalPredicateEntry

"thin" — open scale, contrary to "thick"

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def English.Predicates.Adjectival.deep : AdjectivalPredicateEntry

"deep" — open scale, contrary to "shallow"

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def English.Predicates.Adjectival.shallow : AdjectivalPredicateEntry

"shallow" — open scale, contrary to "deep"

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def English.Predicates.Adjectival.strong : AdjectivalPredicateEntry

"strong" — open scale, contrary to "weak"

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def English.Predicates.Adjectival.weak : AdjectivalPredicateEntry

"weak" — open scale, contrary to "strong"

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def English.Predicates.Adjectival.fast : AdjectivalPredicateEntry

"fast" — open scale, contrary to "slow"

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def English.Predicates.Adjectival.slow : AdjectivalPredicateEntry

"slow" — open scale, contrary to "fast"

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def English.Predicates.Adjectival.old : AdjectivalPredicateEntry

"old" — open scale, contrary to "young"

Equations

• English.Predicates.Adjectival.old = { form := "old", dimension := some Semantics.Gradability.Dimension.age, antonymForm := some "young", antonymRelation := some Features.NegationType.contrary }

def English.Predicates.Adjectival.young : AdjectivalPredicateEntry

"young" — open scale, contrary to "old"

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Sensory adjectives

def English.Predicates.Adjectival.bright : AdjectivalPredicateEntry

"bright" — open scale, contrary to "dark"

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def English.Predicates.Adjectival.dark : AdjectivalPredicateEntry

"dark" — open scale, contrary to "bright"

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def English.Predicates.Adjectival.loud : AdjectivalPredicateEntry

"loud" — open scale, contrary to "quiet"

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def English.Predicates.Adjectival.quiet : AdjectivalPredicateEntry

"quiet" — open scale, contrary to "loud"

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Evaluative adjectives

def English.Predicates.Adjectival.good : AdjectivalPredicateEntry

"good" — open value scale, contrary to "bad". "good" takes a contextual standard and patterns with relative adjectives ([Bel25] §3); on the open .value scale this class is derived (open ⇒ contextual) rather than stipulated, so no standardOverride is needed.

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def English.Predicates.Adjectival.bad : AdjectivalPredicateEntry

"bad" — value scale, contrary to "good"

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def English.Predicates.Adjectival.beautiful : AdjectivalPredicateEntry

"beautiful" — open scale, contrary to "ugly"

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def English.Predicates.Adjectival.ugly : AdjectivalPredicateEntry

"ugly" — open scale, contrary to "beautiful"

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def English.Predicates.Adjectival.important : AdjectivalPredicateEntry

"important" — open scale

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• English.Predicates.Adjectival.important = { form := "important", dimension := some Semantics.Gradability.Dimension.importance }

def English.Predicates.Adjectival.safe : AdjectivalPredicateEntry

"safe" — open scale, contrary to "dangerous"

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def English.Predicates.Adjectival.dangerous : AdjectivalPredicateEntry

"dangerous" — open scale, contrary to "safe"

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Physical disturbance deverbal adjectives

[Tha25]: physical disturbance predicates are associated with a totally closed, multi-point scale. Lower bound = physical instantiation of disturbance; upper bound = spatial extent of host entity. Gradable (more cracked, badly dented), compatible with completely and partially. Contra [RH14] (two-point) and [RW04b] (lower-bounded only).

def English.Predicates.Adjectival.cracked : AdjectivalPredicateEntry

"cracked" — closed scale, contradictory to "uncracked". Deverbal adjective from crack (Levin 45.1 Break verbs). NOT a two-point scale: accepts more cracked, completely cracked, partially cracked, badly cracked ([Tha25] §2.3–2.4).

Equations

• English.Predicates.Adjectival.cracked = { form := "cracked", dimension := some Semantics.Gradability.Dimension.cracking }

def English.Predicates.Adjectival.dented : AdjectivalPredicateEntry

"dented" — closed scale. Deverbal adjective from dent. Accepts more dented, completely dented, badly dented ([Tha25] (11a), (20b)).

Equations

• English.Predicates.Adjectival.dented = { form := "dented", dimension := some Semantics.Gradability.Dimension.denting }

def English.Predicates.Adjectival.scratched : AdjectivalPredicateEntry

"scratched" — closed scale. Deverbal adjective from scratch. Accepts more scratched, completely scratched, badly scratched ([Tha25] (11b), (20c)).

Equations

• English.Predicates.Adjectival.scratched = { form := "scratched", dimension := some Semantics.Gradability.Dimension.scratching }

def English.Predicates.Adjectival.shattered : AdjectivalPredicateEntry

"shattered" — closed scale, NON-GRADABLE. Deverbal adjective from shatter (Levin 45.1 Break verbs). Contrast: ??more shattered, punctual verb, no durative reading. Not a physical disturbance predicate ([Tha25] (12c)).

Equations

• English.Predicates.Adjectival.shattered = { form := "shattered", dimension := some Semantics.Gradability.Dimension.shattering }

Mildly positive adjectives (MPAs)

[Bel25]: MPAs encode a necessity standard — the minimum value required for pursuit. They share properties with both relative (context-sensitive, gradable) and absolute (no zone of indifference, crisp judgments, barely compatible) predicates.

def English.Predicates.Adjectival.nice : AdjectivalPredicateEntry

"nice" — open scale, positive evaluative ([Nou24]). Base for M-degree intensifier nicely.

Equations

• English.Predicates.Adjectival.nice = { form := "nice", dimension := some Semantics.Gradability.Dimension.value, evaluativeValence := some Features.EvaluativeValence.positive }

def English.Predicates.Adjectival.pleasant : AdjectivalPredicateEntry

"pleasant" — open scale, positive evaluative ([Nou24]). Base for M-degree intensifier pleasantly.

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def English.Predicates.Adjectival.decent : AdjectivalPredicateEntry

"decent" — a mildly-positive adjective: open .value scale with a functional (necessity) standard ([Bel25]), recorded via standardOverride.

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def English.Predicates.Adjectival.acceptable : AdjectivalPredicateEntry

"acceptable" — mildly-positive adjective; open .value scale, functional standard ([Bel25]). Deverbal -able form: the modal suffix contributes the functional standard.

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def English.Predicates.Adjectival.adequate : AdjectivalPredicateEntry

"adequate" — mildly-positive adjective; open .value scale, functional (necessity) standard ([Bel25]).

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Deadjectival intensifier bases ([Nou24])

Adjectival bases for deadjectival intensifiers. Evaluative adjectives (horrible, wonderful) derive H-degree or M-degree intensifiers via the Goldilocks effect. Mirative (unusual, surprising) and modal (possible, impossible) bases follow Zwicky's generalization.

def English.Predicates.Adjectival.horrible : AdjectivalPredicateEntry

"horrible" — open scale, negative evaluative. Base for H-degree horribly.

Equations

• English.Predicates.Adjectival.horrible = { form := "horrible", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.negative }

def English.Predicates.Adjectival.terrible : AdjectivalPredicateEntry

"terrible" — open scale, negative evaluative. Base for H-degree terribly.

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• English.Predicates.Adjectival.terrible = { form := "terrible", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.negative }

def English.Predicates.Adjectival.awful : AdjectivalPredicateEntry

"awful" — open scale, negative evaluative. Base for H-degree awfully.

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• English.Predicates.Adjectival.awful = { form := "awful", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.negative }

def English.Predicates.Adjectival.dreadful : AdjectivalPredicateEntry

"dreadful" — open scale, negative evaluative. Base for H-degree dreadfully.

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• English.Predicates.Adjectival.dreadful = { form := "dreadful", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.negative }

def English.Predicates.Adjectival.frightening : AdjectivalPredicateEntry

"frightening" — open scale, negative evaluative. Base for H-degree frighteningly.

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• English.Predicates.Adjectival.frightening = { form := "frightening", dimension := some Semantics.Gradability.Dimension.danger, evaluativeValence := some Features.EvaluativeValence.negative }

def English.Predicates.Adjectival.disgusting : AdjectivalPredicateEntry

"disgusting" — open scale, negative evaluative. Base for H-degree disgustingly.

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• English.Predicates.Adjectival.disgusting = { form := "disgusting", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.negative }

def English.Predicates.Adjectival.annoying : AdjectivalPredicateEntry

"annoying" — open scale, negative evaluative. Base for H-degree annoyingly.

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• English.Predicates.Adjectival.annoying = { form := "annoying", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.negative }

def English.Predicates.Adjectival.unpleasant : AdjectivalPredicateEntry

"unpleasant" — open scale, negative evaluative, contrary to "pleasant".

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def English.Predicates.Adjectival.scary : AdjectivalPredicateEntry

"scary" — open scale, negative evaluative. Base for H-degree scarily.

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• English.Predicates.Adjectival.scary = { form := "scary", dimension := some Semantics.Gradability.Dimension.danger, evaluativeValence := some Features.EvaluativeValence.negative }

def English.Predicates.Adjectival.wonderful : AdjectivalPredicateEntry

"wonderful" — open scale, positive evaluative. Base for M-degree wonderfully.

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• English.Predicates.Adjectival.wonderful = { form := "wonderful", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.positive }

def English.Predicates.Adjectival.delightful : AdjectivalPredicateEntry

"delightful" — open scale, positive evaluative. Base for M-degree delightfully.

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• English.Predicates.Adjectival.delightful = { form := "delightful", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.positive }

def English.Predicates.Adjectival.gorgeous : AdjectivalPredicateEntry

"gorgeous" — open scale, positive evaluative. Base for M-degree gorgeously.

Equations

• English.Predicates.Adjectival.gorgeous = { form := "gorgeous", dimension := some Semantics.Gradability.Dimension.beauty, evaluativeValence := some Features.EvaluativeValence.positive }

def English.Predicates.Adjectival.unusual : AdjectivalPredicateEntry

"unusual" — open scale, neutral (mirative), contrary to "usual".

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def English.Predicates.Adjectival.surprising : AdjectivalPredicateEntry

"surprising" — open scale, neutral (mirative). Base for H-degree surprisingly.

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• English.Predicates.Adjectival.surprising = { form := "surprising", dimension := some Semantics.Gradability.Dimension.expectation, evaluativeValence := some Features.EvaluativeValence.neutral }

def English.Predicates.Adjectival.remarkable : AdjectivalPredicateEntry

"remarkable" — open scale, positive evaluative (§2.4.1). Extreme positive evaluation: H-degree remarkably despite positive valence (Goldilocks exception).

Equations

• English.Predicates.Adjectival.remarkable = { form := "remarkable", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.positive }

def English.Predicates.Adjectival.stunning : AdjectivalPredicateEntry

"stunning" — open scale, positive evaluative (Figure 2, upper-right quadrant). Extreme positive evaluation: H-degree stunningly (Goldilocks exception).

Equations

• English.Predicates.Adjectival.stunning = { form := "stunning", dimension := some Semantics.Gradability.Dimension.quality, evaluativeValence := some Features.EvaluativeValence.positive }

def English.Predicates.Adjectival.usual : AdjectivalPredicateEntry

"usual" — open scale, neutral (modal), contrary to "unusual".

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def English.Predicates.Adjectival.expected : AdjectivalPredicateEntry

"expected" — open scale, neutral (modal). Unattested as intensifier (*expectedly).

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• English.Predicates.Adjectival.expected = { form := "expected", dimension := some Semantics.Gradability.Dimension.expectation, evaluativeValence := some Features.EvaluativeValence.neutral }

def English.Predicates.Adjectival.possible : AdjectivalPredicateEntry

"possible" — open scale, neutral (modal), contradictory to "impossible".

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def English.Predicates.Adjectival.impossible : AdjectivalPredicateEntry

"impossible" — open scale, neutral (modal), contradictory to "possible".

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def English.Predicates.Adjectival.allEntries : List AdjectivalPredicateEntry

All adjectival predicate entries

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def English.Predicates.Adjectival.lookup (form : String) : Option AdjectivalPredicateEntry

Look up an entry by form

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• English.Predicates.Adjectival.lookup form = List.find? (fun (x : English.Predicates.Adjectival.AdjectivalPredicateEntry) => x.form == form) English.Predicates.Adjectival.allEntries

Derived Kennedy classification

The scale shape, positive standard, and Kennedy class are GradableAdjective views derived from each entry's dimension + pole/override — nothing here is a stored field ([Ken07], [KMcN05]). Everything closes by rfl/decide, so the migration off the old stored scaleType is checked.

theorem English.Predicates.Adjectival.tall_open : Semantics.Gradability.GradableAdjective.scaleType tall = Core.Order.Boundedness.open_

theorem English.Predicates.Adjectival.wet_closed : Semantics.Gradability.GradableAdjective.scaleType wet = Core.Order.Boundedness.closed

theorem English.Predicates.Adjectival.dry_closed : Semantics.Gradability.GradableAdjective.scaleType dry = Core.Order.Boundedness.closed

theorem English.Predicates.Adjectival.wet_min : Semantics.Gradability.GradableAdjective.standard wet = Degree.PositiveStandard.minEndpoint

theorem English.Predicates.Adjectival.dry_max : Semantics.Gradability.GradableAdjective.standard dry = Degree.PositiveStandard.maxEndpoint

theorem English.Predicates.Adjectival.tall_relative : Semantics.Gradability.GradableAdjective.adjectiveClass tall = Degree.AdjectiveClass.relativeGradable

theorem English.Predicates.Adjectival.good_relative : Semantics.Gradability.GradableAdjective.adjectiveClass good = Degree.AdjectiveClass.relativeGradable

theorem English.Predicates.Adjectival.full_absMax : Semantics.Gradability.GradableAdjective.adjectiveClass full = Degree.AdjectiveClass.absoluteMaximum

theorem English.Predicates.Adjectival.straight_absMax : Semantics.Gradability.GradableAdjective.adjectiveClass straight = Degree.AdjectiveClass.absoluteMaximum

theorem English.Predicates.Adjectival.dry_absMax : Semantics.Gradability.GradableAdjective.adjectiveClass dry = Degree.AdjectiveClass.absoluteMaximum

theorem English.Predicates.Adjectival.empty_absMin : Semantics.Gradability.GradableAdjective.adjectiveClass empty = Degree.AdjectiveClass.absoluteMinimum

theorem English.Predicates.Adjectival.wet_absMin : Semantics.Gradability.GradableAdjective.adjectiveClass wet = Degree.AdjectiveClass.absoluteMinimum

theorem English.Predicates.Adjectival.bent_absMin : Semantics.Gradability.GradableAdjective.adjectiveClass bent = Degree.AdjectiveClass.absoluteMinimum

theorem English.Predicates.Adjectival.decent_mildlyPos : Semantics.Gradability.GradableAdjective.adjectiveClass decent = Degree.AdjectiveClass.mildlyPositive

theorem English.Predicates.Adjectival.acceptable_mildlyPos : Semantics.Gradability.GradableAdjective.adjectiveClass acceptable = Degree.AdjectiveClass.mildlyPositive

theorem English.Predicates.Adjectival.adequate_mildlyPos : Semantics.Gradability.GradableAdjective.adjectiveClass adequate = Degree.AdjectiveClass.mildlyPositive

theorem English.Predicates.Adjectival.tall_requires_cc : Semantics.Gradability.GradableAdjective.IsRelative tall

theorem English.Predicates.Adjectival.good_requires_cc : Semantics.Gradability.GradableAdjective.IsRelative good

theorem English.Predicates.Adjectival.wet_no_cc : ¬Semantics.Gradability.GradableAdjective.IsRelative wet

theorem English.Predicates.Adjectival.full_no_cc : ¬Semantics.Gradability.GradableAdjective.IsRelative full

theorem English.Predicates.Adjectival.decent_no_cc : ¬Semantics.Gradability.GradableAdjective.IsRelative decent

theorem English.Predicates.Adjectival.all_gradable : tall.IsGradable ∧ full.IsGradable ∧ wet.IsGradable ∧ good.IsGradable ∧ decent.IsGradable

Every entry above carries a scalar dimension, so all are gradable.