Page 328 - Encyclopedia of Philosophy of Language

Formal Semantics
Harry
NP S/(S\NP)
cooked
and
Mary ate
some apples (16)
Type-raising corresponds semantically to the com- binator T, defined at (8c). It will be shown later that type-raising is quite general in its application to NPs, and that it should be regarded as an operation of the lexicon, rather than syntax, under which all types corresponding to functions into NP (etc.) are replaced by functions into the raised categories). However, for expository simplicity it will continue to be shown in derivations, indexing the rule as > T. When the raised category composes with the transitive verb, the result is guaranteed to be a function which, when it reduces with an object some apples, will yield the same interpretation that would have obtained from the tra-
Harry will copy, and file without reading, (18) some articles concerning Swahili.
Under the simple assumption with which this article began, that only like 'constituents' can conjoin, the substring file without reading must be a constituent formed without movement or deletion. What is more, it must be a constituent of the same type as a transitive verb, VP/NP, since that is what it coordinates with. It follows that the grammar of English must include the following operation (19), first proposed by Sza- bolsci:
Backward Crossed Substitution (<Sx) (19)
Harry will
s/yp
copy and file
yp/NP conj yP/NP
VP/NP S/NP
Y/Z
without
(X\Y)/Z~SX/Z
reading,
some articles (20)
NP
ditional derivation. This interpretation might be writ- ten as follows (17):
cook' apples' harry'. (17) (Here again a convention of'left associativity' is used,
to (cook' apples') harry .) It is important to notice that it is at the level of the interpretation that traditional constituents like the VP, and relations such as c-com- mand, continue to be embodied. This is an important observation since as far as surface structure goes, both have now been compromised.
Of course, the same facts guarantee that the coor- dinate example above will deliver an appropriate interpretation.
The third and final variety of combinatory rule is motivated by examples like (7c), repeated here (18):
This rule permits the derivation shown in (20) for sentence (18). (Infinitival and gerundival predicate categories are abbreviated as VP and VPing, and NPs are shown as ground types.)
It is important to notice that the crucial rule resembles a generalized form of functional compo- sition, but that it mixes the directionality of the functors, combining a leftward functor over VP with a rightward function into VP. Therefore it must be predicted that other combinatory rules, such as com- position, must also have such 'crossed* instances. Such rules are not valid in the Lambek calculus.
Like the other combinatory rules, the substitution rule combines the interpretations of categories as well as their syntactic categories. Its semantics is given by the combinator S, defined at (8g). It follows that if the constituent file without reading is combined with an
so that the above applicative expression is equivalent 1
306
(S\NP)/NP
S/NP
conj
S/NP
NP (S\NP)/NP S/(S\NP)
S/NP
<&>
NP
(VP\VF)IVPing (vp\yp)/Np
yp/Np
-<&>
yPing/NP