A Common Derivation for Parsing and Generation with Expectation-Based Minimalist Grammars (e-MGs)
Authors: Cristiano Chesi (IUSS, 2021)
Topic: Lexical and Semantic Resources and Analysis

Abstract
Expectation-based Minimalist Grammars (e-MGs) are simplified versions of the (Conflated) Minimalist Grammars, (C)MGs, formalized by Stabler (Stabler 1997; Stabler 2011; Stabler 2013) and Phase-based Minimalist Grammars, PMGs (Chesi 2007; Chesi 2005; Stabler 2011). The crucial simplification consists of driving structure building only using lexically encoded categorial top-down expectations. The commitment on a top-down procedure (in e-MGs and PMGs, as opposed to (C)MGs, Chomsky, 1995; Stabler, 2011) allows us to define a core derivation that is the same in both parsing and generation (Momma & Phillips 2018).

Introduction
Minimalism (Chomsky 1995; Chomsky 2001) is an elegant transformational grammatical framework that defines structural dependencies in phrasal (i.e. hierarchical) terms simply relying on one core structure building operation, Merge, that combines lexical items and the result of other Merge operations. (1).a is the representative result of two ordered Merge operations (i.e. Merge(γ, Merge(α, β)) both taking the items α, β and γ directly from the lexicon, while (1).b relies on the so called Internal Merge (Move): the re-Merge of an item that was already merged in the structure. As result, Move connects the item at the edge of the structure (β) with a trace (_β), a phonetically empty copy of the item that in a previous Merge operation combined with a hierarchically lower item (α in (1).b). In both (Conflated) Minimalist and Phase-based Minimalist Grammars ([C]MGs and PMGs respectively) Merge and Move are feature-driven operations, that is, a successful operation must be triggered by the relevant (categorial) features matching, and, once these features are used, they get deleted. Consequently, a feature pair is always responsible for each operation (unless specific features are left unerased after a successful operation, as in raising predicates and successive cyclic movement, Stabler 2011). One crucial difference between PMGs and MGs is that while MGs operate from-bottom-to-top, as indicated in (2), PMGs structure building operations apply top-down as schematized in (3): Another relevant difference between the two approaches is related to the implementation of Move: MGs use the “+/-” feature distinction and the same deletion procedure after matching, while PMGs do not use “-” features and simply assume that both “+” and “=” select categorial features, which are deleted after Merge. In PMGs, “+” features force memory storage and hence the movement (downward) of the licensed item, until the relevant prominent category identifying the moved item (Z in (3)) is selected. If no proper selection is found, the sentence is ungrammatical. CMG as well dispenses the grammar with the +/- feature distinction and only relies on select features (=X), but it must assume that feature deletion can be procrastinated (again, for instance, in raising predicates). Despite the fact that, from a generative point of view, all these formalisms are equivalent and they all fall under the so called mildly-context sensitive domain (Stabler 2011), it is worth to appreciate the dynamics of structure building “on-line”, namely how the derivation unrolls, word by word. Taking the MGs lexicon (4), the expected constituents in (1) are built adding items to the left-edge of the structure at each Merge/Move application, as described in (5). An equivalent structure is obtained in PMGs as shown in (7). Notice a minimal difference in the lexicon (6): the absence of the “-” features. The result of the two derivations is (strongly) equivalent in hierarchical (and dependency) terms. The simplicity, in pre-theoretical terms, of the two descriptions is comparable: while PMGs must postulate the M storage to implement Move (as result of the missing selection of a categorial feature), MGs must postulate independent workspace to build nontrivial left-branching structures, for instance before merging a multi-word subject like “the boy” with its predicate (e.g., “runs”). Furthermore, both formalisms must restrict the behavior either of the M buffer operativity or the accessibility to the -f features to limits the Move operation (e.g., island constraints, Huang, 1982).ambiguation strategies do not alter the general derivation procedure introduced here, which remains the lowest common denominator of Generation and Parsing in e-MGs.

Conclusion
The e-MGs formalization proposed here is a simple (parametrized) framework for comparing syntactic predictions directly with human parsing and generation performance evidence. This is possible since the core derivation algorithm is assumed to be the same in both tasks (token transparency, Miller & Chomsky 1963). While there is little to add to implement a full-fledged Generation procedure (see §3.2), as long as the Parsing perspective is concerned, the information asymmetry of this task with respect to Generation requires extra routines to be implemented, in addition to the basic derivation algorithm: lexical ambiguity must be resolved “on-line” and phonetically empty items must be postulated when needed. This creates an extra level of complexity which is however manageable under the same derivational perspective here presented: the core derivation is sufficiently specified to operate independently from parsing-specific disambiguation assumptions which operate monotonically with respect to Merge, Move and Agree. This is an ideal foothold for metrics that aim at comparing the predicted difficulty not only globally (De Santo, 2020; Graf et al., 2017) but also “on-line” that is, on a word by word basis (Chesi & Canal 2019; Chesi 2021).