Lexical Semantics of Adjectives - CiteSeerX

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As we already established in Sections 3.3-4 above, the LEX-MAPs of the adjectives truly derived
from verbs or nouns (deverbals and denominals, respectively) are created from the LEX-MAPs of
the corresponding verbs or nouns with the help of lexical rules.
The remaining adjectives are scalars, and the task we face is to assign each of them to an appropriate
scale. Obviously, with each new adjective, we must decide if it fits into an existing scale or it
requires the addition of a new scale. Before answering this question, let us discuss the conditions
of “membership” in a scale.
There are two types of scale, as we know, numerical ones and literal ones (see also Section 3.3). If
we suspect that the adjective we are processing belongs on an existing numerical scale we must
place it there with a certain numerical value, which in most cases will be greater than that of some
other adjectives and less than that of still others. We can then check on the comparative constructions
involving these adjectives.
Thus, if the currently-processed adjective is minuscule and the candidate scale is, of course, SIZE,
and we tentatively place the adjective on the scale with a value greater than microscopic but less
than itty-bitty (109), then the two comparative statements in (110) should obtain.
(109) microscopic < minuscule < itty-bitty
(110) (i) X is minuscule, Y is microscopic: therefore X is bigger than Y.
(ii) X is minuscule, Y is itty-bitty: therefore X is smaller than Y.
If the existing scale is literal, such as, for instance SHAPE (see (61)), the operation is a little more
evolved. What is true for the different values on a literal scale is that no object can have two of
them at the same time (111). (112), a generalization of (111) is not, however, a sufficient condition
for Y and Z to belong on the same scale because Y and Z may be very different in meaning but
incapable to modify the same type of noun; thus, for instance, if Y = round and Z = psychological,
the former may define only physical-objects and the latter only mental-objects. Something like
(113) will definitely work for the SHAPE scale, and some variation of its generalized formula (114)
should work for other literal scales as well.
(111) X cannot be both round and square.
(112) X cannot be both Y and Z.
(113) X cannot be both round and square, and round and square are both shapes.
(114) X cannot be both Y and Z, and Y and Z are both [scale-name N or NP].
It may seem that the second propositions of (113-114) should suffice to determine the membership
of an adjective on a literal scale, but if, for instance, our current adjective is rectangular and we
have already placed square on the SHAPE scale, (115) will incorrectly accept the former adjective
as another value on the scale but it will fail the (112/114) test in (116), prompting a more complicated
resolution of such a case (e.g., replace the square value on the scale with the more general
rectangular value).
(115) Rectangular and square are both shapes.
(116) *X cannot be both rectangular and square.
These considerations about literal scales guide the postulation of a new literal scale. If we are processing
the adjective front and we don’t have a scale for it, we must first come up with related ad-