The behaviour of adverbs and adjectives has qualities of both ordinary selection and something else, something unique to modifiers. This makes them difficult to model. Modifiers are generally optional and transparent to selection while arguments are required and driven by selection. Cinque (1999) proposed that adverbs, functional heads, and descriptive adjectives are underlyingly uniformly ordered across languages and models them by ordinary Merge or selection. Such a model captures only the ordering restrictions on these morphemes; it fails to capture their optionality and transparency to selection. I propose a model of adjunction with a separate Adjoin function that allows the derivation to keep track of both the true head of the phrase and the place in the Cinque hierarchy of the modifier, preventing inverted modifier orders in the absence of Move

Keywords: adjoin, minimalist grammars, adjectives, adverbs, functional projections, ordering, optionality

Classical Minimalist Grammars have only one type of Merge, based on selection. A similistic kind of adjunction can be captured in the same way that categorial grammars handle modifiers: by both selecting and returning the same category (e.g. features =XX). While this captures the optionality and repearablity of adjuncts, it fails to capture the ordering restrictions some adjuncts have, and also shifts the head of the phrase to the modifier.

The Cinquean approach to capturing adjunct order can be modeled with Merge: each functional head selects the one below it, and each has a variant that selects an adjunct in its specifier, thus capturing the ordering restrictions of some adjuncts. However, the optionality is captured only by multiplying the lexicon to include variants with and without specifiers; worse, in order for the functional heads to keep their order, each head must have an additional variant with neither meaning nor pronunciation: just a piece of syntactic glue to hold the structure together. Such an approach misses generalisations, and misses the special character of adjuncts, which are clearly different from arguments.

I propose that adjuncts be treated separately from arguments, adding to the grammar sets of adjunct categories for each syntactic category, a distinct operation Adjoin, and category tuples that use numbers to track the hierarchy level of the last adjunct adjoined to the phrase. Adjoin is undefined when a new adjunct is lower in teh hierarchy than the adjuncts already present.

This hierarchy tracking can also be extended to Adger's Hierarchy of Precedence (HoP) Merge, as outlined in my dissertation chapter

                
@phdthesis{fowlie2017slaying,
  title={Slaying the Great Green Dragon: Learning and modelling iterable ordered optional adjuncts},
  author={Fowlie, Meaghan},
  year={2017},
  school={UCLA}
}
            

                
@inproceedings{fowlie-2013-order,
    title = "Order and Optionality: {M}inimalist {G}rammars with Adjunction",
    author = "Fowlie, Meaghan",
    booktitle = "Proceedings of the 13th Meeting on the Mathematics of Language ({M}o{L} 13)",
    month = aug,
    year = "2013",
    address = "Sofia, Bulgaria",
    publisher = "Association for Computational Linguistics",
    url = "https://www.aclweb.org/anthology/W13-3002",
    pages = "12--20",
}
            

                
@inproceedings{Fowlie14,
  author    = {Meaghan Fowlie},
  editor    = {Glyn Morrill and
               Reinhard Muskens and
               Rainer Osswald and
               Frank Richter},
  title     = {Adjuncts and Minimalist Grammars},
  booktitle = {Formal Grammar - 19th International Conference, {FG} 2014, T{\"{u}}bingen,
               Germany, August 16-17, 2014. Proceedings},
  series    = {Lecture Notes in Computer Science},
  volume    = {8612},
  pages     = {34--51},
  publisher = {Springer},
  year      = {2014},
  url       = {https://doi.org/10.1007/978-3-662-44121-3\_3},
  doi       = {10.1007/978-3-662-44121-3\_3},
}