Editing Distributed morphology (section)

==Distributed morphology approach to core theoretical issues==

===Morpheme order===

In Distributed Morphology, the linear order of morphemes is determined by their hierarchical position in the syntactic structure, as well as by certain post-syntactic operations. Head movement is the main syntactic operation determining morpheme order, while Morphological Merger (or Merger under Adjacency) is the main post-syntactic operation targeting affix order. Other post-syntactic operations that might affect morpheme order are Lowering and Local Dislocation (see previous section for details on these operations).

====Head movement====
Head movement is subject to the Head Movement Constraint, according to which when a head moves, it cannot skip an intervening head. Left adjunction and the Head Movement Constraint ensure that the Mirror Principle holds. The syntactic mechanism responsible for the effects of the Mirror Principle is head movement: heads raise and left-adjoin to higher heads. The general principle behind morpheme order is the Mirror Principle (first formulated by Baker 1985), according to which the linear order of morphemes is the mirror image of the hierarchy of syntactic projections. For example, in a plural noun like ''cat-s'', the plural morpheme is higher in the hierarchy than the noun: [<sub>NumP</sub> -s[<sub>NP</sub> cat]]. The Mirror Principle dictates that the linear order of the plural morpheme with respect to the noun should be the mirror image of their hierarchy, namely the attested ''cat-s''. 
Research subsequent to Baker (1985) has shown that there are some apparent violations to the Mirror Principle and that there are more operations involved in the determination of the final linear order of morphemes. Firstly, the left adjunction requirement of head movement has been relaxed, as right adjunction has been shown to be possible (Harley 2010 among others{{by whom|date=March 2019}}). Therefore, different heads can have a specification for right vs. left adjunction. We could imagine, for example, that there is a language in which head movement of the noun to the Number head is specified for right adjunction, rather than left adjunction which is the case in English. In that language, the predicted order of the noun and plural morpheme would then be ''s-cat''. Notice, however, that right vs. left adjunction determines whether an affix will be realized as a prefix or a suffix: its closeness to the root will still reflect hierarchical order. Let's look at a hypothetical example to make this clear. Assuming that Tense is merged higher than Aspect, there are four possible orders for the tense and aspect morphemes with respect to the verb stem, once we allow for variation between left and right adjunction in head movement.

# Verb – Aspect – Tense
# Tense – Verb – Aspect 
# Aspect-Verb-Tense
# Tense-Aspect-Verb

Crucially, though, the following two orders are predicted to be impossible.

# Aspect-Tense- Verb 
# Verb – Tense – Aspect

These orders are the orders in which the tense morpheme is closer to the root than the aspect morpheme. Since Aspect is merged before Tense and morpheme order still reflects hierarchical order, such a configuration is predicted to be impossible.

Finally, certain post-syntactic operations can affect morpheme order. The best studied one is Morphological Merger or Merger Under Adjacency. This operation merges two adjacent terminal nodes into one morphological word. In other words, it allows for two heads which are adjacent to merge into one word without syntactic head movement – the operation is post-syntactic. This operation is doing the work of, say, affix lowering of the past tense morpheme in English in early generative syntax. For the operation to apply, what is crucial is that the morphemes to be merged are linearly adjacent.

===Allomorphy===

A core idea in deriving allomorphy in Distributed Morphology is underspecification. Verbal agreement in the present tense in English takes the form /-s/ in the 3rd person singular (‘ex. John eats bologna’), and /Ø/ in all other cases (‘I eat bologna;’ ‘They eat bologna’). The phonological exponents of the feature bundle terminal nodes in the syntactic tree are listed in the Exponent List. We can capture the fact that /-s/ has a much smaller distribution than /Ø/ using the following entries in the Exponent List:

#[3sg, present] ↔ /-s/
#[present] ↔ /Ø/

/-s/ will be inserted whenever its full featural specification is met. In all other cases in the present tense however, such as [2sg, present] or [1sg, present], /Ø/ will be inserted. This is a use of underspecification, the idea that there is a ‘default’ morpheme that is inserted in the general case, and more specific morphemes that are inserted in more specific cases, when their featural specifications are met. In the above example, /Ø/ is underspecified in the sense that it is not specified for person. Underspecification relies on the ‘Maximal Subset Condition.’ <ref name="ReferenceA"/>

The Maximal Subset Condition states firstly that, for a given exponent E to be inserted into some feature bundle T, the featural specification on E must be a subset of the features on T. In this way, /-s/ is not a possible exponent for a feature bundle [2sg, present]. However, /Ø/ is a possible exponent for the feature bundle [3sg, present]. To ensure that /-s/ is chosen over /Ø/ for the bundle [3sg, present], the Maximal Subset Condition states secondly that, between two exponents E and F which both contain a subset of the features in a feature bundle T, the exponent that contains the maximal subset of the features in T will be selected.

Featural specification derives allomorphy in featural paradigms. Allomorphy in which different phonological exponents of the same feature bundle are idiosyncratically realized depending on the morphological or phonological environment is captured through contextual specification. An example of such allomorphy is the English plural marker. The typical English plural marker is /-z/, as in bulls. However, the plural of child is children, and the plural of cactus is cacti. Since the choice of the plural morpheme exponent is not related to features, but rather simply to the root it attaches to, the roots must be listed in the contextual specification:
#[-sg] ↔ /-z/
#[-sg] ↔ /-ren/ / _ {child}
#[-sg] ↔ /-i/ / _ {cact}

If the contextual specification of some item is met, it is inserted. Otherwise, insert the item that has no contextual specification. This is an example of the ‘elsewhere condition’.<ref name="ReferenceA"/> Note that the Maximal Subset Condition stated above is a formal instantiation of the elsewhere condition.

Contextual specification is also used to account for phonologically conditioned suppletive allomorphy, using phonological contexts. Thus, the singular indefinite marker in English can be stated as follows (we could also underspecify one of the allomorphs to express a default morpheme):

#[-def, +sg] ↔ an / _V
#[-def, +sg] ↔ a / _C

A prediction about suppletive allomorphy in Distributed Allomorphy is that, assuming exponents are inserted in a bottom-up fashion of the syntactic tree, it should always be ‘inward-looking.’ This means that contextual allomorphy can only involve the selection of an allomorph based on something lower in the tree. That is, the contextual environments must always involve items lower in the tree.

Morphologically conditioned allomorphy may involve [[suppletion]] (as in ''go-Ø/wen-t'') or readjustment rules that apply in the context of certain Vocabulary items (as in ''buy-Ø/bough-t'').  Suppletion and readjustment rules apply to a terminal node and its associated Vocabulary item – unlike affixation, which combines this terminal node with a separate terminal node that has its own distinct (though potentially null) Vocabulary item.  Suppletion arises from the competition of Vocabulary items for insertion into a terminal node.  Competition involving root Vocabulary items is a topic of ongoing research, however.  Early work in Distributed Morphology suggests that a single, abstract lexical root appears in the syntax; in this view, roots do not compete for insertion into root nodes, but exist in free variation, constrained only by semantic and pragmatic well-formedness.  Subsequent research has suggested that the distribution of root Vocabulary items can be grammatically restricted (Embick 2000, Pfau 2000, Marantz 2013); this means that roots may be featurally restricted and thus subject to competition.  The issue of whether root alternations such as ''buy-Ø/bough-t'' are better handled by suppletion or readjustment rules remains a topic of debate (Embick & Marantz 2008, Siddiqi 2009, Bonet & Harbour 2012).

The term ''suppletion'' refers to allomorphy of an open-class lexical item. For a large-scale study of suppletion in the context of comparative and superlative adjectival morphology within the general framework of Distributed Morphology, see Bobaljik (2012).<ref name=":0">Bobaljik, Jonathan David (2012). Universals In Comparative Morphology: Suppletion, Superlatives, and the Structure of Words. Cambridge, MA: MIT Press.</ref>

=== Containment hypothesis ===
The containment hypothesis is a theory under the framework of Distributed Morphology advanced by Bobaljik (2012) to account for the restrictions on the patterns of [[suppletion]] seen in language. It states:<blockquote>''"The representation of the superlative properly contains that of the comparative (in all languages that have a morphological superlative)."''<ref name=":0" /></blockquote>Bobaljik argues that if a language has a [[superlative]] form, it must build off the comparative form. In other words, the superlative form and the bare adjective cannot be built off the same root to the exclusion of the comparative (a so-called *ABA pattern), because the comparative is necessarily ''contained'' within the superlative form. Thus, languages allow:
# AAA: All three forms to be built off the same adjectival root
# ABB: The comparative and superlative are suppletive and thus built off a different root from that of the bare adjective
# ABC: The bare adjective, comparative, and superlative are all built off different roots
{| class="wikitable"
!Pattern
!'''Language'''
!Adjective
!'''Comparative'''
!Superlative
|-
| rowspan="3" |AAA
|[[Persian language|Persian]]
|X
|X-tær
|X-tær-in
|-
|[[Hungarian language|Hungarian]]
|X
|X-bb
|leg-X-bb
|-
|[[Chukchi language|Chukchi]]
|X
|X-əŋ
|ənan-X-əŋ
|-
| rowspan="2" |ABB
|[[English language|English]]
|good
|better
|best
|-
|[[Czech language|Czech]]
|špatn-ý
'bad'
|hor-ší
'worse'
|nej-hor-ší
'worst'
|-
|ABC
|[[Latin]]
|bonus
'good'
|melior
'better'
|optimus
'best'
|}
The exclusion of the *ABA pattern means that there should theoretically exist no language with a pattern analogous to *''good – better – goodest''. AAB patterns (in which the superlative is suppletive but the comparative builds off the bare adjective) are theoretically possible as well but happen to be rare in the world's languages. Under the model of Distributed Morphology, the structure of a superlative would be [<sub>SPRL</sub> [<sub>CMPR</sub> [<sub>ADJ</sub> Adjective ] Comparative ] Superlative ]. Thus, the exponent of the comparative morpheme attaches to the bare adjective and the exponent of the superlative morpheme attaches to the comparative form (or replaces it in the suppletive cases). The following rules may be posited for Czech as an example:<ref name=":1" />
# √BAD → špatn-
# √BAD → hor- / ___ CMPR
# CMPR → -ší
# SPRL → nej-
Rule 2 above states that the root BAD is suppleted in the environment of a comparative. By extension, the superlative form attaches the prefix ''nej-'' to ''horši'' and not to ''špatn-'' as the comparative is the only structure it can see. For Latin, in which both the comparative ''and'' the superlative are suppleted, the following rules may be posited:<ref name=":1" />
# √GOOD → bon-
# √GOOD → mel- / ___ CMPR
# √GOOD → opt- / ___ SPRL
# CMPR → -ior
# SPRL → -imus
As an *ABA pattern would require the adjective to directly combine with the superlative node, it is theoretically impossible because of the intervening comparative node and is also unattested in the world's languages. Nevins (2015) supports the structure by arguing that the semantics of the superlative is dependent on that of the comparative.<ref name=":1" />
# Comparative: Y is more ADJ than X
# Superlative: For all X, Y is more ADJ than X
The comparative definition is contained within the superlative one and thus, the superlative must obligatorily subsume it in its structure.

===Morphological paradigms===

In Distributed Morphology morphological paradigms are seen as epiphenomena. Irregular forms or gaps associated with paradigms are explained via competition for vocabulary insertion.<ref name=McGinnis/>

===Meaning in Distributed Morphology===

In Distributed Morphology there are two different types of meaning: the meaning associated with the bundles of features of the Lexicon and the idiosyncratic meaning listed in the Encyclopedia. It is believed that encyclopedic meaning is associated with lexical roots, rather than with complete phrases.<ref name=McGinnis/>

===Allosemy===

Allosemy – the phenomenon in which a single morpheme can have multiple semantic realizations – is handled the same way allomorphy is handled in DM: through contextual specification and the Elsewhere Condition. The Encyclopedic List contains the semantic meaning and context for each entry in the list. When a single morpheme is realized with multiple possible meanings, it has multiple entries in the Encyclopedic List. Thus, we can derive multiple possible meanings of ‘look’  with the following entries:  (note:   √  indicates square root, CAPS LOCK indicates semantic concept)

#√ look ←→ PHYSICAL APPEARANCE / [__]V Adj
#√ look ←→ NOTABLE GLANCE / [__]N  <!--sp NOTABLE ?-->
#√ look ←→ CONSULT A SOURCE / [ __ up]V 
#√ look ←→ λ x, λ y, y looks at x / elsewhere

	The contextual specifications for  √ look will ensure that it has the appropriate interpretation given the context. The contextual specifications can only include various pieces of information, such as the word class of the item, the word class of a sister node, or even the specific morpheme of the sister node. However, it cannot contain any information about a non-sister node (although there will be some complications when a word intervenes between a word and the relevant sister node ex. “look the book up.”). And, just as in the Exponent List, an item in the Encyclopedic List can be specified as being inserted ‘elsewhere:’ in all contexts where the contextual specification of all other entries for that morpheme are not met. Besides expressing the notion of a ‘default’ semantic meaning of a given morpheme, having the elsewhere condition as an explicit contextual specification also allows for the expression of morphemes that do not have a default semantic meaning.
	For many English speakers, ‘cahoot’ only has an interpretation when preceded by ‘in’ (ex. John was in cahoots with the Russians.) The entry for ‘cahoot’ might have the following entry for such a context:

#√ cahoot ←→ CONSPIRACY / [  in [ ___ -sg ] ]
 	
	To express the fact that this is the only context where cahoot has a meaning, we simply posit that there is no entry for cahoot with the elsewhere condition for its contextual specification. Thus, by allowing for the omission of the elsewhere specification, we can express the fact that certain morphemes require a specific context for interpretation.
	We can use contextual specification to model other aspects of idiomatic meaning, namely, the fact that idiomatic meaning often does not hold across different syntactic configurations.  The expression the shit hit the fan loses its idiomatic meaning if passivized: #the fan was hit by the shit. We can express this fact by specifying voice on the contextual specification for the verb:

#√ hit ←→BECOME AN EXTREME SITUATION / [voiceactive [ ____ fan]]

	Finally, just as in allomorphy, the Maximal Subset Principle will play a part if the contextual specification for one alloseme is a subset of another alloseme. While the following entries for eat, meant to express two possible meanings for the phrase eat up (ex. John ate up the story vs. John ate up all his food), are not necessarily the exact specifications, they illustrate a hypothetical use of the Maximal Subset Condition:

#√ eat ←→ ENJOY / [ ____ up] [non-food object]
#√ eat ←→ FINISH THE FOOD / [ ____ up]
 
	The FINISH THE FOOD entry for √ eat will be inserted whenever eat up is followed by any food object. However, when eat up is followed by a non-food object, both entries’ contextual specifications will be met. However, the ENJOY entry is inserted, because more conditions in its contextual specification are met. Thus, the Maximal Subset Condition will choose the alloseme whose contextual specification is most completely satisfied, when there is competition among Encyclopedic List entries.<ref name="ReferenceA"/>

=== Crosslinguistic variation ===

Since the model of Distributed Morphology consists of three lists (Formative List, Exponent List, Encyclopedia), we expect crosslinguistic variation  to be located in all three of them. The feature bundles and their structure might be different from language to language (Formative List), which could affect both syntactic and post-syntactic operations. Vocabulary Items (Exponent List) can also be different crosslinguistically. Finally, the interpretation of roots (Encyclopedia) is also expected to show variation.