At the nexus between computation and theory:
In his dissertation research, Yohei Oseki investigated how to model the recognition of visually presented morphologically complex words. In the most promising model that he confronted with behavioral and MEG data, words were parsed by a probabilistic context free grammar of morphological structure, from left to right in the word. Cumulative surprisal over the word, given the correct parse, correlated with reaction time in lexical decision and with brain responses around 170ms post-stimulus onset around the Visual Word Form Area of the left hemisphere.
In his PCFG, category nodes dominating stems and derivational affixes were treated as non-terminals, with the orthographic form of morphemes identified as the terminals. So in parsing, say, “parseability,” at the second morphological form in the parse, -abil, the relevant rules would be one that expands an adjective into a verb and an adjective head ([Adj[v[parse]]Adj]) and an “emission” rule that expands the Adj node into -abil. At -ity, the emission rule that takes the non-terminal N node to -ity would not be sensitive to the presence of “-abil” under the Adj node. From the perspective of a speaker’s knowledge of English, this is wrong – speakers know that “able/abil” potentiates nominalizing -ity.
If we were to improve the model, we probably would want to stick closely to the actual structure of Distributed Morphology, since the development of DM involves maximum consideration of all potentially relevant types of data – formal choices within the theory are motivated by empirical considerations. In DM, the phonological/orthographic form of a morpheme is a vocabulary item. Vocabulary insertion is part of the Phonology, separate from the Merger operation that builds structures from morphemes. So, we would like to model “emission” not as a context free operation, as might be appropriate for structure building, but as a context sensitive insertion rule (so, in early versions of transformational syntax, lexical insertion was a transformation, rather than a PS rule). On this approach, the category nodes of the morphological tree are potentially terminal nodes – vocabulary insertion doesn’t create a (non-branching) tree structure but elaborates the terminal node into which it is inserted. This matters for locality: we want -ity to be inserted as a sister to -able, so -able must reside at the A node, not below it.
A context dependent vocabulary insertion rule seems formally equivalent to a treelet – N <-> -ity in the context of [Adj able ] = [N[Aable] ity] Or, rather, the rule looks like a fragment tree in a Fragment Grammar, since the -able can be the head of the adjective, sister to a verbal head – the relevant subtree is not a proper tree structure. Which raises the question of the formal connection between PCFGs with contextual rules of vocabulary insertion and TAG and Fragment Grammar formalisms.
For the moment, I’m thinking about a couple quasi empirical questions. First, if we’re considering continuations of, say, a verb “parse,” does the frequency in which adjectives are made from verbs overall in English really contribute to the processing of “parseable” over and above the transition probability from “parse” to “able”? One could ask similar questions about sentential parsing, and perhaps people have – is the parsing of a continuation from a transitive verb to its direct object modulated by the probability of a transitive verb phrase in general in English, independent of the identity of the head verb?
Second is a theoretical question about the representation of derivational morphemes, with possible computational consequences. It’s clear that many derivational affixes contribute meanings beyond those associated with bare category nodes. So “-able” has a meaning beyond that of a simple adjective head. A possibility being explored in the morpho-phonological literature is that (many) derivational heads include roots. However, this possibility comes with the additional possibility that there’s a split between root-full derivational heads and derivational morphemes that are the pure spell out of category heads. So, for example, maybe the little v that verbalizes many Latinate stems in English and is spelled out as -ate is a pure category head, without a root. A further speculation is that such bare category heads might be classed with inflectional heads, and exhibit contextual allosemy – meaning that they could have null interpretations. Jim Wood’s recent work on Icelandic (and English) complex event nominalizations suggests that nominalizers of verbs may have null interpretation – these nominalizers, then, would be candidates for the bare category head type of derivational suffix, while contentful nominalizers such as -er would always involve roots and would not show the null semantic contextual allosemy of the bare nominalizers.