An efficient Trie for binding (and movement)
Authors: Cristiano Chesi (IUSS, 2018)
Topic: Syntax and Dependency Treebanks

Abstract
Non-local dependencies conEnglish. Non-local dependencies connecting distant structural chunks are often modeled using (LIFO) memory buffers (see Chesi 2012 for a review). Other solutions (e.g. slash features in HPSG, Pollard & Sag 1994) are not directly usable both in parsing and in generation algorithms without undermining an incremental leftright processing assumption. Memory buffers are however empirically limited and psycholinguistically invalid (Nairne 2002). Here I propose to adopt Trie memories instead of stacks. This leads to simpler and more transparent solutions for establishing non-local dependencies both for whargumental configurations and for anaphoric pronominal coreference.

Introduction
Relations among structural chunks in a sentence are not always resolvable using strictly local dependencies. This is the case of argumental wh items in languages like English (or Italian), where the argument and the predicate can be arbitrarily distant, (1).a. Another case of non-local dependency is pronominal coreference that in some cases can also be cross-sentential, (1).b-b', (1).b-b''. (1) a. [X Cosa] (tu) pensi che (io) [Y mangi_]? what (you) think that (I) eatSUBJ-1P-Sing what do you think I eat? b. [X Gianni]i saluta [Z Mario]j. G. says hello (to) M. b'. Poi pro i [Y si]i lava. then (he) himselfj washes. then he washes himself b''. Poi pro i [Y lo]j lava. then (he) himj washes. then he washes him From a purely structural perspective, the chunks X and Y enter a non-local dependency relation when some material Z intervenes between them. A long tradition of different approaches addressed this issue from different perspective (see Nivre 2008, for instance, for a comparison among Stack-based and List-based algorithms in parsing). Most of the time these approaches rely on transformations of the grammar into a deductive system for both parsing (Shieber et al. 1995) and generation (Shieber 1988). A loss of transparency with respect to the linguistic intuitions that motivated a specific grammatical formalism is then at issue. Here I will argue in favor of a simple derivational and deterministic perspective in which phrases are considered the result of the recursive application of structure building operations (Chomsky 1995). In its simplest format, classic structural descriptions, (2).a, reduce to lexicalized trees, (2).a', in which x and z creates a constituent (get merged) either if x selects z (=z x, in Stabler’s 1997 formalism) or the way around (=x z). Leaves are linearly ordered and constituents labels reduce to the selecting lexical items. (2) a. a'. By definition, x and y cannot enter a local dependency whenever an intervening item z blocks a local selection between x and y. There are cases, however, in which x and y should enter a local selection relation: in (1).a, x receives a thematic role from y, hence y should select x according to the uniformity of theta-role assignment hypothesis (Baker 1988). In this case, a non-local dependency must be established. Implementing the movement metaphor (Stabler 1997) in top-down terms, Chesi (2017) proposes that an item x is moved into a Last-In-First-Out (LIFO) memory buffer (M) whenever it brings into the computation features that are unselected: if a (categorial) feature X is selected and a lexical item a brings X but also Y from the lexicon (i.e. [X Y a]]), then a gets merged (i.e. [X[X Y a]]), but the unselected feature [Y (a)] is moved into the last position (the most prominent one) of the M-buffer. As soon as a feature Y will be selected (=Y), the last item in the memory buffer, if bearing the relevant Y category, will be remerged in the structure before any other item from the lexicon, the satisfying a local selection requirement. After its re-merge, the item is removed from the M-buffer. This paper proposes a theoretical solution for simplifying this memory-based approach without losing any descriptive adequacy: here I will do away with the buffer idea (and, as a consequence, with the LIFO restrictions) by postulating a memory Trie (Fredkin 1960) based on the features merged in the structure during the derivation. I will show that this solution is psycholinguistically more plausible than LIFO buffers used so far and computationally sound.

Conclusion
In this paper, I presented a revision of the memory buffer used for parsing and generation in PMGs: instead of using a classic LIFO memory, proved to be sufficient to capture locality effects (Friedmann et al. 2009) when “similar” NPs are processed (Warren & Gibson 2005, Chesi 2017), but not fully plausible from a psycholinguistic perspective (no serial order seems to be relevant at retrieval, Nairne 2002, as we saw also in case of pronominal binding), I defined a Trie memory replacement, based on feature hierarchies sensitive to the structural insertion point of the memorized item. This prevents order of insertion from being strictly relevant at retrieval, without losing any ability to discriminate the correct items to be recalled for establishing a relevant (non-local) structural dependency both in thematic role assignment or anaphoric binding contexts. The Trie structure here proposed is clearly a bit simplistic, though based on a relevant evidence suggesting that person features are “higher” in the structure than “number” features (Mancini et al. 2011). Other (semantic) features should be included (e.g. animacy) as well as prosodic/salience markers (Topic, New Information/Contrastive Focus, Kiss 1998) that clearly play a role in making salient (i.e. unique in a Trie) a specific item, possibly relating the “fluctuation” of prominence of items stored in memory (Lewis & Vasishth 2005) to precise structural proprieties.