Paracompositionality, MWEs and Argument Substitution

This is equivalent to saying that in CCG the type is not always an abbrevation for , which might be the case in other brands of categorial grammars. The English facts above could be taken care of by featural distinctions such as in , rather than also positing a . But in ergative languages the does not always coincide with the same LF role as it does in English, such as in Dyirbal’s control construction, where the controlled absolutive argument can be the patient NP of the transitive clause or syntactic subject of an intransitive clause, but not the ergative NP of the transitive clause. It seems to require where x’s role in the controlled clause is determined by verbal morphology of the controlled clause; see [22] for the phenomenon. Assuming a cross-linguistically makes narrower predictions about control. We handle this problem elsewhere.

TAG transformations take a phrase structure tree and decompose it to elementary structures to deliver an LF. [21] is a different TAG way to incorporate meaning postulates of [25]. HPSG uses phrasal post-classification to the same effect. For example [4, 27] perform it at the final stage of parsing as a semantic check on bags of predicates for idiom entries, and [17] use semantic frame identification, viz. compositional vs idiomatic, which are built in to theory. The diversity of approaches in the volume for idioms [14] is testimony to the practice that the idioms are decisive factors in polishing our theories linguistically, psychologically and computationally.

van der Linden [32], which is another categorial approach to idioms, allows vacuous abstractions, i.e. define semantics without mention of x in the LF of (7b). Apart from our empirical claim that they have a place in LF because they relate to contingency, vacuous abstractions seem to open ways to resource insensitivity which is unheard of in natural language; for example, the  combinator with its vacuous abstraction \(\lambda x\lambda y.x\) can delete things from LF. We have yet to find a word or morpheme that does this; see [5]:81 for some speculation.

[32]’s treatment of phrasal idioms such as kick the bucket assumes partial involvement of the head verb kick for the semantics of the idiom, whereas in our conception it is fully responsible for the idiom with the aid of singleton types.

We show only one directional variant of each rule for brevity. The same idea applies to all variants; see Steedman references for a standard set of rules, and [5] for review of proposals for combinatory extensions.

Bozşahin [5]: Sect. 10 shows that all projection rules of CCG can be packed into one monad to enable monadic computation with just one rule of projection. This is possible because CCG is radically lexicalized in the sense that combinatory rules cannot project anything which is not in the lexicon. What appears to be rule choice when presented as (9/13) becomes dependency passing within monad with one rule of combination.

The way this is implemented in many CCG systems including ours is for example to constrain the slashes as follows:

It is easier to describe slash-modal control from the perspective of syntactic types of expressions accessing these rules. ‘\(\star \)-rules’ are accessible by all categories, ‘\(\diamond \)’ and ‘\(\times \)’ are compatible only with themselves, and with the most permissive slash.

The fact that this form is also attested in child and adult language suggests that these entries may be bonafide lexical options.

It is tempting to try for kick the proverbial bucket which is a head-subcategorizing category; but, we would have to overextend ourselves to eliminate the idiom reading in kick the proverbial bucket that overflowed if we have to. In this sense we suggest that phrasal idioms are best treated with singleton types.

One way to put it altogether is to use a feature such as \(\mp \)special in addition to h, which ordinary verbs negatively specify, heads of idiomatic combination positively specify, and heads of syntactic constructions eg. coordinators and relative markers (under)specify as they see fit. The value ‘+special’ need not be further broken down for singletons because they are self-representing, and, presumably, featureless. For example phonological weight is intrinsically captured in ; also, lexical content.