Nanosyntax

Phrasal spellout. The idea that any node in the tree can correspond to a lexical item. Put differently, spellout applies to syntactic phrases, and syntactic phrases are the things that are stored in lexical entries. (This is a restrictive vew of spanning - spanning only targets constituents - and is opposed to the more liberal 'sequential spanning', see below). Phrasal spellout has its origin in Starke's work on -ABLE and -ED.

The Superset Principle. The idea that a lexical item can spellout syntactic structures which are smaller than that lexical item. More precisely, the structure contained in the lexical item can be bigger than the structure that it lexicalises. In such cases, the lexical item is a superset of the syntactic structures being spelled out. This means that one given lexical item can in principle spell out a range of different syntactic structures (as long as it is bigger or equal to those syntactic structures)

Span / spanning. A lexical item is said to span a syntactic structure if it corresponds to a continuous sequence in that structure. 'Spanning' is a cover term for two more specialised hypotheses competing with each other: sequential spanning and phrasal spellout (or 'phrasal spanning')

Sequential spanning. The hypothesis that you can spellout an arbitrary stretch of the syntactic structure, as long as it forms a continuous stretch. This means that you can spellout non-constituents. This is in opposition to "phrasal spellout", see above. This hypothesis is found in the work by Abels/Muriungi on the Kitharaka focus marker, and has its origin outside nanosyntax, in Williams' 2003 work. (An even earlier remote cousin is Brody's mirror principle work, though Brody's notion is more restrictive than sequential spanning in that it is structural. It is in fact intermediate between phrasal spellout and sequential spanning)

Underassociation. Underassociation is mostly another term for the Superset Principle. More precisely, you can think of it as the result of applying the superset principle non-vacuously: when part of the structure in a lexical item is unused for the spellout of a given syntactic structure, that unused piece is "underassociated".

Here are some more specialised terms floating around in the nanosyntax world:

The *ABA. Informally: if a given span is lexicalised by A, and a slightly bigger version of this span is lexicalised by B, then it is impossible for A to lexicalise a span even bigger than B. This generalisation is formulated by Bobaljik, and it follows from the superset principle operating on an ordered fseq (functional sequence of features). Caha's work on the nanosyntax of case makes extensive use of the *ABA theorem to deduce the structure of case from the syncretisms found in case systems.

The Identification principle. This is a hypothesised restriction constraining the superset principle. The idea is that no piece of the lexical item can be truly missing. If a piece appears to be missing, it is because it is lexicalised by some other lexical item. The metaphor is that the missing pieces have to be "identified" by some other lexical item in order to be legitimately missing. This hypothesis is found in Ramchand's book "First phase syntax"

Maximise span. When a given syntactic node could be spelled out either by two smaller lexical items or one bigger lexical item, the bigger one wins. The intuition behind the name is that the bigger one has a bigger span, so the one with the maximal span ends up winning. (This is also called 'overriding', see below). This competition principle derives Poser's generalisation.

Minimise Junk. When two lexical items are in competition to spellout a given span/subtree (because they both contain that span/subtree), the one which wins is the one which contains the least unused material, ie the least junk. This principle is sometimes also called "best fit": the lexical entry which contains the span/tree fitting most tightly the target syntactic structure is the one which wins

Overriding. In a cyclic bottom-up spellout, spelling out a higher constituent 'overrides' any earlier spellout of a smaller subpart of that constituent. This is a derivational way of deriving the 'maximise span' principle without postulating any principle other than the derivation itself

Pointers. In some cases, a lexical item contains another lexical items (or 'refers to' another lexical item). Idioms are clear cases of this: the whole idiom is a lexical item (since it is associated to an arbitrary meaning), but its constituent words are independently existing lexical items. The lexical entry for the idiom is said to contain 'pointers' in the nodes corresponding to the independently existing words in the idiom. Thus the lexical entry for 'kick a bucket' will have a pointer in the N/NP projection , which points to the independently existing lexical entry for 'bucket'