Editing Minimalist program (section)

== Beyond basic operations ==

=== Label ===
A substantial body of literature in the minimalist tradition focuses on how a phrase receives a proper label.<ref>{{Cite book|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/9780470755662|title=Derivation and Explanation in the Minimalist Program|date=2002|publisher=John Wiley & Sons, Ltd|isbn=9780470755662|editor1-last=Epstein|editor1-first=Samuel David|edition=1|doi=10.1002/9780470755662|editor2-last=Seely|editor2-first=T. Daniel}}</ref> The debate about labeling reflects the deeper aspirations of the minimalist program, which is to remove all redundant elements in favour of the simplest analysis possible.<ref name="lowe2020">{{Cite journal|last1=Lowe|first1=John|last2=Lovestrand|first2=Joseph|date=2020-06-29|title=Minimal phrase structure: a new formalized theory of phrase structure|url=http://jlm.ipipan.waw.pl/ojs/index.php/JLM/article/view/247|journal=Journal of Language Modelling|volume=8|issue=1|pages=1|doi=10.15398/jlm.v8i1.247|issn=2299-8470|doi-access=free}}</ref> While earlier proposals focus on how to distinguish adjunction from substitution via labeling, more recent proposals attempt to eliminate labeling altogether, but they have not been universally accepted.

'''Adjunction and substitution''': Chomsky's 1995 monograph entitled ''The Minimalist Program'' outlines two methods of forming structure: [[Adjunct (grammar)|adjunction]] and substitution. The standard properties of segments, categories, adjuncts, and specifiers are easily constructed. In the general form of a structured tree for adjunction and substitution, α is an adjunct to X, and α is substituted into SPEC, X position. α can raise to aim for the X<sup>max</sup> position, and it builds a new position that can either be adjoined to [Y-X] or is SPEC, X, in which it is termed the 'target'. At the bottom of the tree, the minimal domain includes SPEC Y and Z along with a new position formed by the raising of α which is either contained within Z, or is Z.<ref name="chomsky1995">{{cite book|last1=Chomsky|first1=Noam|title=The Minimalist Program|date=1995|publisher=MIT Press|location=Cambridge MA}}</ref>[[File:Adjunction and Substitution.png|200x200px|Adjunction and Substitution|left]]'''Adjunction''': Before the introduction of bare phrase structure, adjuncts did not alter information about bar-level, category information, or the target's (located in the adjoined structure) [[headedness|head]].<ref name="biolinguistics.eu|journal">{{Cite journal|last1=Hornstein|first1=Norbert|last2=Nunes|first2=Jairo|date=2008|title=Adjunction, Labeling, and Bare Phrase Structure|url=http://www.biolinguistics.eu|journal=[[Biolinguistics]]|volume=2|issue=1|pages=057–086 |doi=10.5964/bioling.8621 |s2cid=54832701 |doi-access=free}}</ref> An example of adjunction using the X-bar theory notation is given below for the sentence '''''Luna bought the purse yesterday'''''. Observe that the adverbial modifier '''''yesterday''''' is sister to VP and dominated by VP. Thus, the addition of the modifier does not change information about the bar-level: in this case the maximal projection VP. In the minimalist program, adjuncts are argued to exhibit a different, perhaps more simplified, structure. Chomsky (1995) proposes that adjunction forms a two-segment object/category consisting of: (i) the head of a label; (ii) a different label from the head of the label. The label L is not considered a term in the structure that is formed because it is not identical to the head S, but it is derived from it in an irrelevant way. If α adjoins to S, and S projects, then the structure that results is L = {<H(S), H(S)>,{α,S}}, where the entire structure is replaced with the head S, as well as what the structure contains. The head is what projects, so it can itself be the label or can determine the label irrelevantly.<ref name="chomsky1995" /> In the new account developed in bare phrase structure, the properties of the head are no longer preserved in adjunction structures, as the attachment of an adjunct to a particular XP following adjunction is non-maximal, as shown in the figure below that illustrates adjunction in BPS. Such an account is applicable to XPs that are related to multiple adjunction.<ref name="biolinguistics.eu|journal" />

:::Adjunction<sub>DEFINITION</sub>: <'''H'''(S), '''H''' (S)>, where Label = {<H(S), H(S)>,{α,S}} (S = head)

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'''Substitution''' forms a new category consisting of a head (H), which is the label, and an element being projected. Some ambiguities may arise if the features raising, in this case α, contain the entire head and the head is also X<sup>MAX</sup>.<ref name="chomsky1995" />
:::Substitution<sub>DEFINITION</sub>: Label = {'''H'''(S), {α,S}).
'''Labeling algorithm''' ('''LA'''): Merge is a function that takes two objects (α and β) and merges them into an unordered set with a label (either α or β), where the label indicates the kind of phrase that is built via merge. But this labeling technique is too unrestricted since the input labels make incorrect predictions about which lexical categories can merge with each other. Consequently, a different mechanism is needed to generate the correct output label for each application of Merge in order to account for how lexical categories combine; this mechanism is referred to as the ''labeling algorithm'' (LA).<ref name=":9">{{Cite book|last=Narita|first=Hiroki|url=https://www.taylorfrancis.com/chapters/edit|title=Merge, Labeling, and Projection|date=2017|publisher=Routledge|isbn=9781315442808|edition=1|pages=94–118|doi=10.4324/9781315442808-5}}</ref>

* '''Labeling via selection and agreement'''. In a series of articles, Chomsky has proposed that labels are determined by a labeling algorithm which operates after syntactic structures have been built. This mechanism departs from previous version of generative grammar in that the labels of a phrase are now determined [[Endocentric and exocentric|endocentrically]]. There are a number of proposals that have been hypothesized to explain the exact nature of the labeling algorithm. In earlier discussions, Chomsky hypothesizes that determining the label of a set-theoretic object (α, β) depends on either semantic selection or agreement holding between α and β. Although this formulation of the LA is consistent with the basic principles of X-bar theory, reference to external relations like semantic selection and agreement are at odds with the goal of developing a parsimonious account.
:::Labeling Algorithm (version 1): The output of Merge (α, β) is labeled by α if:
:::(a) α '''selects''' β as its semantic argument, or
:::(b) α '''agrees''' with β, meaning, β is led to α because of Spec-head agreement (feature checking) (Chomsky 1995b;2000)

* '''Labeling via external and internal Merge'''. Proposed by Chomsky in 2008, in this version of LA, clause (a) means that the output of Merge(V, DP) would be labelled V because V is a lexical item. Clause (b) means that if a syntactic object is re-introduced into the derivation via internal Merge—as it is when a subject DP moves to Spec,TP—then the output of Merge(DP,T) would be labelled T. However, this version of LA uses a disjunctive definition of labelling, one for external Merge (clause a), and one for internal merge (clause b).
:::Labeling algorithm (version 2): The output of Merge (α, β) is labeled by α if
:::(a) α is a lexical item (LI), or
:::(b) β is internally merged to α (Chomsky 2008: 145)

* '''Labeling via prominence'''. Chomsky (2013) suggests an even simpler LA based on the notion of "prominence". In this version of the LA, the label is independently determined by whichever properties of UG ([[universal grammar]]) allow us to identify a "prominent Lexical Item.  Due to this revision, it becomes questionable whether Merge plays any role at all in labelling/projection, since it is now redundant.
:::Labeling algorithm (version 3): The label/head of an SO (syntactic object) Σ is the most prominent Lexical Item within Σ. (Chomsky 2013)

* '''Labeling via set formation''': Further simplification is given in Chomsky (2000), where Merge is simplified to an elementary set-formation operation, meaning that syntactic objects (SOs) are no longer associated with non-terminal nodes, like projections. Labels are now only the syntactically relevant "head" of a phrase that are determined independently by the LA. With this theory, labeling leaves bare phrase structure (BPS) completely projection-free.

:::Labeling algorithm (version 4): Merge(α, β) =  {α, β}.

Recently, the suitability of a labeling algorithm has been questioned, as syntacticians have identified a number of limitations associated with what Chomsky has proposed.<ref name="narita2021">{{cite book|last1=Narita|first1=Hiroki|title=Symmetrizing Syntax: Merge, Minimality, and Equilibria|last2=Fukui|first2=Naoki|date=2021|publisher=Routledge Studies in Linguistics|pages=129–188}}</ref> It has been argued that two kinds of phrases pose a problem. The labeling algorithm proposes that labelling occurs via minimal search, a process where a single lexical item within a phrasal structure acts as a head and provides the label for the phrase.<ref>{{cite journal|last1=Chomsky|first1=Noam|date=2013|title=Problems of Projection|journal=Lingua|volume=130|pages=33–49|doi=10.1016/j.lingua.2012.12.003|s2cid=3060970 }}</ref> It has been noted that minimal search cannot account for the following two possibilities:<ref name="narita2021" />

# {H, H} where both constituents are lexical items.
# {XP, YP} where neither constituent is a lexical item.

In each of these cases, there is no lexical item acting as a prominent element (i.e. a head). Given this, it is not possible through minimal search to extract a label for the phrase. While Chomsky has proposed solutions for these cases, it has been argued that the fact that such cases are problematic suggests that the labeling algorithm violates the tenets of the minimalist program, as it departs from conceptual necessity.

Other linguistic phenomena that create instances where Chomsky's labeling algorithm cannot assign labels include predicate fronting, embedded topicalization, scrambling (free movement of constituents), stacked structures (which involve multiple specifiers).

Given these criticisms of Chomsky's labeling algorithm, it has been recently argued that the labeling algorithm theory should be eliminated altogether and replaced by another labeling mechanism. The symmetry principle has been identified as one such mechanism, as it provides an account of labeling that assigns the correct labels even when phrases are derived through complex linguistic phenomena.<ref name="narita2021" />

=== Agree ===
Starting in the early 2000s, attention turned from feature-checking as a condition on movement to feature-checking as a condition on agreement. This line of inquiry was initiated in Chomsky (2000), and formulated as follows:

::Agree: α can agree with β if and only if:
:::(a) α carries at least one unvalued and uninterpretable feature and
::::β carries a matching interpretable and valued feature
:::(b) α c-commands β
:::(c) β is the closest goal to α
:::(d) β bears an unvalued uninterpretable feature (from Zeijlstra 2012)

Many recent analyses assume that Agree is a basic operation, on par with Merge and Move. This is currently a very active area of research, and there remain numerous open questions:<ref>{{Cite book|last1=Smith|first1=Peter W.|title=Agree to Agree: Agreement in the Minimalist Programme|last2=Mursell|first2=Johannes|last3=Hartmann|first3=Katharina|chapter=Some remarks on agreement within the Minimalist Programme |publisher=Language Science Press|year=2020|editor-last=Smith|editor-first=Peter W.|publication-place=Berlin|pages=1–29|doi=10.5281/zenodo.3541743|isbn=9783961102143 |editor-last2=Mursell|editor-first2=Johannes|editor-last3=Hartmann|editor-first3=Katharina}}</ref>

# Is Agree a primitive operation?
# What is the "direction" of the Agree relation: does it apply top-down, bottom-up, or both?
# Is Agree a syntactic operation, a post-syntactic operation that applies at PF, or both?
# Is the Agree relation restricted to certain feature types?
# Is the Agree relation subject to locality restrictions?
# Which phenomena are best modelled by the Agree relation?
# Is the Agree relation conditioned by other factors, or does it apply freely?
# How does Agree interact with other operations such as Merge and Label?

Co-indexation as feature checking: co-indexation markers such as {k, m, o, etc.}<ref name="sportiche2014" />
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