51.04.01 · linguistics / syntax-sentence-structure

Syntax — constituency, dependency, and generative grammar

shipped3 tiersLean: none

Anchor (Master): Chomsky 1957 Syntactic Structures (Mouton); Chomsky 1965 Aspects of the Theory of Syntax (MIT Press); Chomsky 1995 The Minimalist Program (MIT Press); Carnie 2013 Syntax

Intuition Beginner

Syntax is the part of linguistics that studies how words combine into sentences. It does not ask what words mean or how they sound — those are semantics and phonology. It asks one question: what are the rules of combination that make a sentence well-formed?

The key idea is that a sentence is more than a flat string of words. It has hidden structure. The words group into phrases, and those phrases group into larger phrases, until the whole sentence is one big phrase. A reader or speaker uses this hidden grouping, not just the word order, to recover the meaning.

Two sentences can have the same words in the same order and yet mean different things. That is the strongest evidence for hidden structure: if language were just a sequence of words, there would be nothing to be ambiguous about.

This unit introduces three lenses on sentence structure: grouping words into phrases (constituency), linking words head-to-dependent (dependency), and the generative program that treats syntax as a rule system powerful enough to describe every sentence of a language and only those.

Visual Beginner

The classic ambiguity "I saw the man with the telescope" has two hidden structures. In one, the telescope is the instrument I used; in the other, it is something the man was holding.

The two structures differ in a single attachment point. That single difference flips the meaning, which is direct evidence that sentences carry structure that word order alone cannot show.

Worked example Beginner

Consider the sentence "I saw the man with the telescope." It has two readings.

Reading A (instrument). I used a telescope, and through it I saw the man. The phrase "with the telescope" attaches to the action "saw".

Reading B (possession). I saw a particular man — the one holding a telescope. The phrase "with the telescope" attaches to the noun "the man".

We draw each structure with labeled brackets. The difference is exactly where the prepositional phrase (PP) "with the telescope" hangs.

Reading A — PP attaches high, to the verb phrase:

[S [NP I] [VP [VP [V saw] [NP the man]] [PP [P with] [NP the telescope]]]]

Reading B — PP attaches low, inside the object noun phrase:

[S [NP I] [VP [V saw] [NP [NP the man] [PP [P with] [NP the telescope]]]]]

Same nine words, same order, two trees. The trees predict two meanings, and speakers reliably get both. That is the phenomenon syntax exists to explain.

Check your understanding Beginner

Formal definition Intermediate+

A phrase-structure grammar (a context-free grammar in the sense of 47.01.05) is a quadruple $G = (N, Σ, P, S)$ where $N$ is a finite set of non-terminal categories (S, NP, VP, PP, ...), $Σ$ is a finite set of terminal symbols (the words), $P$ is a finite set of production rules of the form $A \to β$ with $A \in N$ and $β \in (N \cup Σ)^{*}$ , and $S \in N$ is the start symbol. The language $L (G)$ is the set of terminal strings derivable from $S$ by repeated rule application. A derivation licenses a phrase-structure tree whose interior nodes are non-terminals and whose leaves, read left to right, are the yielded string ^{[Hopcroft Motwani Ullman 2001]}.

A constituent of a tree is any sub-tree, equivalently any string dominated by a single non-terminal node. Constituency is diagnosed empirically by the stand-alone, movement, replacement, and coordination tests: a string is a constituent to the extent it can answer a question, appear sentence-initially, be replaced by a pro-form, or be conjoined with a like string ^{[Carnie 2013]}.

A dependency tree instead labels each word with a single head-dependent arc; it has one node per word and forbids the grouping into multi-word phrases. Formally a dependency analysis is a labelled rooted tree on the word string with a single root and with each non-root word having exactly one head ^{[Tallerman 2015]}. Constituency and dependency are not rival notations for the same object: they make different empirical commitments about, for instance, whether a verb and its object form a unit to the exclusion of the subject.

The Chomsky hierarchy partitions the phrase-structure grammars by the shape of their rules into four nested classes:

Type 3 — regular: $A \to a B$ or $A \to a$ (right-linear). Equivalent to finite automata 47.01.01.
Type 2 — context-free: $A \to β$ (a single non-terminal on the left). Equivalent to pushdown automata 47.01.05.
Type 1 — context-sensitive: $α A β \to α γ β$ with $∣ γ ∣ \geq 1$ .
Type 0 — recursively enumerable: unrestricted rules; equivalent to Turing machines.

These nest: regular $\subset$ context-free $\subset$ context-sensitive $\subset$ recursively enumerable, a strict chain each level of which is provable by a pumping- or decidability argument 47.01.04.

Counterexamples to common slips

Linear order is not structure. "Dog bites man" and "Man bites dog" share vocabulary but differ in both structure and truth conditions; the structure encodes who did what.
A dependency tree is not "just" a phrase-structure tree drawn without phrase nodes. The two disagree on testable predictions (e.g. whether the verb+object form a constituent), so the choice is empirical, not cosmetic.
Context-free does not mean "free of context." It means rules rewrite a single symbol regardless of its neighbours; the name marks a restriction on rule shape, not a claim about meaning.

Key concepts Intermediate+

X-bar theory. In the standard model of ^{[Chomsky 1965]}, every phrase is built around a single head projected through a fixed geometry: the head $X^{0}$ projects to an intermediate bar-level $X^{'}$ and then to a maximal phrase XP. Complements are sisters of the head inside $X^{'}$ ; specifiers and adjuncts attach at the XP or $X^{'}$ level. The schema XP → (specifier) X'; X' → X (complement) uniformises phrase structure across categories, so that noun phrases, verb phrases, and prepositional phrases all share one architecture.

Movement and transformations. A single sentence has two relevant representations: a deep structure (where arguments receive their thematic roles) and a surface structure (where they are pronounced). Long-distance dependencies — questions ("What did Mary think that Bill said __?"), relatives, passives, topicalisations — are modelled by moving a constituent from its base position to a structural position higher in the tree, leaving a trace (__) behind. Movement is structure-dependent: it targets phrases, never arbitrary substrings, and it obeys locality constraints (islands).

The Minimalist Program. The current generative framework ^{[Chomsky 1995]} reduces the computational system to one operation, Merge, which takes two syntactic objects and forms a set from them, recursively building trees of unbounded size from a finite lexicon. A later, constrained variant Internal Merge re-merges an already-built object, generating movement ("copy") for free. A second relation, Agree, establishes feature-checking between a probe and a goal, which underlies case, agreement, and displacement. The empirical content of the program is the claim that the richness of cross-linguistic syntax follows from Merge, Agree, and a small set of economy conditions, with parametric variation narrowed to the features of functional heads.

A non-generative position: construction grammar. Against the autonomy thesis, Construction Grammar ^{[Goldberg 1995]} and the usage-based work of Langacker and Tomasello deny that syntax is an independent, innate module. On this view the basic units are constructions — conventionalised form-meaning pairings of varying generality, from morphemes to idioms to abstract argument-structure patterns (the ditransitive, the caused-motion pattern). Generalisations emerge from categorising token utterances, not from applying a priori rules; a sentence is well-formed to the degree it instantiates licensed constructions. The contested question — is syntax autonomous? — thus has at least two well-developed answers: yes (generative), and no, syntax is the structured residue of constructions and use (constructional/usage-based).

Bridge. This treatment builds toward 51.05.01 (semantics), where the syntactic tree becomes the input to compositional interpretation, rule by rule, and appears again in 47.01.05 (context-free grammars), whose hierarchy classifies exactly which tree-configurations a phrase-structure grammar can generate. The central insight is that syntax is the layer that mediates sound and meaning, this is exactly why a finite grammar can describe an unbounded set of sentences, and putting these together, the bridge is that the same tree-configurations recur in parser design, categorial grammar, and the proof theory of type-logical systems.

Exercises Intermediate+

Exercise 7 (hard, symbolic).

State two empirical predictions that distinguish a constituency analysis from a dependency analysis of the sentence "The student solved the problem quickly," and say which result would favour which framework.

Hint

Consider whether "solved the problem" behaves as a unit (movement, replacement) and whether the adverb attaches to the verb or to the whole predicate.

Answer

Prediction 1 — verb-object constituency: constituency theory groups [solved the problem] as a VP constituent, so it should be replaceable by "did so" ("the student did so quickly") and movable as a unit. If these tests succeed, constituency is supported; a pure dependency tree, which admits no VP node, must explain the unit-like behaviour by other means. Prediction 2 — adverb attachment: if "quickly" modifies the event as a whole, constituency places it as a VP-adjunct; dependency must attach it directly to the verb as a dependent. A contrast in scope (does "quickly" modify "solved" or "solved the problem"?) thus pulls the two analyses apart.

Exercise 8 (hard, symbolic).

State the autonomy of syntax thesis and give one argument for it (generative) and one argument against it (constructional/usage-based).

Hint

Autonomy says syntactic generalisations are stated over form alone, independent of meaning and use.

Answer

Autonomy thesis: syntactic well-formedness is governed by a system of formal rules over syntactic categories that is independent of semantics and of frequency of use. For: structure-dependent operations such as question formation ("Is the man who is tall ___ happy?") apply over hierarchical structure, not linear order or meaning, and hold across speakers who have never heard the sentence — suggesting a form-only computational system. Against: construction grammarians observe that argument-structure patterns carry stable meanings (the ditransitive conveys transfer) and that grammaticality gradients track frequency and analogy, so form and meaning are inseparable and syntax is the residue of learned, meaningful constructions rather than an autonomous module.

Lean formalization Intermediate+

lean_status: none. The unit's formal backbone — context-free grammars, the strict Chomsky hierarchy, and the regular/context-free separation — belongs to formal-language theory and is treated on the computer-science side in 47.01.04 and 47.01.05. The linguistic core (constituency tests, X-bar geometry, Merge/Agree, the autonomy debate) is empirical and prose-gated, so no Lean module is attached here.

Advanced results Master

Where natural language sits in the hierarchy. Chomsky's original argument ^{[Chomsky 1957]} was that English is not captured by finite-state (regular) models: centre-embedding and long-distance agreement require unbounded pushdown-style memory. The consensus placement of most natural-language syntax is at or near the context-free level, with cross-serial dependencies in Swiss-German verb clusters and in certain agreement patterns argued by Shieber (1985) to be mildly context-sensitive — strictly above context-free yet below general context-sensitive. The modern reconciliation uses mildly context-sensitive formalisms (tree-adjoining grammars, combinatory categorial grammar, minimalism grammars), which are weakly equivalent in expressive power and polynomially parsable.

Closure and decidability by level. Context-free languages are closed under union, concatenation, and Kleene star, and under intersection with a regular language, but not under intersection or complement; this non-closure is the engine behind the separation proofs. Decidability tracks the hierarchy: membership, emptiness, and finiteness are decidable for context-free languages but undecidable for context-sensitive and recursively enumerable ones. These bounds set the computational floor for parsing: a grammar that overgenerates into Type 0 buys expressivity at the cost of undecidable well-formedness 47.01.04.

The competence–performance distinction. Generative syntax separates the idealised speaker-hearer's grammatical system (competence) from the real-time resource limits of speaking and understanding (performance). This is what licenses formal models of unbounded centre-embedding even though speakers degrade on depth three: the grammar generates the strings, while the parser — a bounded-memory mechanism studied in psycholinguistics — fails to process them. The distinction is also the fault line of the autonomy debate, since usage-based theorists read performance-level frequency gradients as evidence against a clean competence module.

Synthesis. The hierarchy and movement analyses developed here build toward 47.01.05, where context-free grammars are characterised by the pumping lemma and pushdown automata, and appears again in 51.05.01, where syntactic structure feeds compositional semantic interpretation. The foundational reason natural language sits near the context-free tier is that nesting and agreement obey bounded locality, this is exactly the structural fact the minimalist program captures with Merge and Internal Merge, the pattern generalises to the mildly context-sensitive parsers used in computational linguistics, and putting these together, the bridge is that syntax supplies the combinatorial skeleton on which phonology, semantics, and processing all hang.

Full proof set Master

Proposition. The language $L = {a^{n} b^{n} : n \geq 1}$ is context-free but not regular.

Proof (context-free). Consider the grammar $G$ with productions $S \to a S b ∣ ab$ . A derivation applies $S \to a S b$ some $k \geq 0$ times and then $S \to ab$ once, yielding $S \Rightarrow a S b \Rightarrow \dots \Rightarrow a^{k} S b^{k} \Rightarrow a^{k + 1} b^{k + 1}$ . Every derived string is therefore $a^{n} b^{n}$ with $n = k + 1 \geq 1$ , so $L (G) \subseteq L$ . Conversely, for any $a^{n} b^{n} \in L$ with $n \geq 1$ , take $k = n - 1$ applications of $S \to a S b$ followed by $S \to ab$ ; this derives $a^{n} b^{n}$ . Hence $L \subseteq L (G)$ , and $L (G) = L$ .

Proof (not regular). Suppose for contradiction that $L$ were regular, and let $p \geq 1$ be its pumping length. Take $w = a^{p} b^{p} \in L$ , so $∣ w ∣ = 2 p \geq p$ . By the pumping lemma, $w$ admits a split $w = x y z$ with $∣ x y ∣ \leq p$ , $∣ y ∣ \geq 1$ , and $x y^{i} z \in L$ for every $i \geq 0$ . Because $∣ x y ∣ \leq p$ , the substring $x y$ lies entirely inside the initial block of $a$ 's, so $y = a^{j}$ for some $1 \leq j \leq p$ . Pump with $i = 2$ : $x y^{2} z = a^{p + j} b^{p}$ . This string has more $a$ 's than $b$ 's, so it is not of the form $a^{n} b^{n}$ , contradicting the pumping lemma. Therefore $L$ is not regular. ∎

Remark. The counter pattern $a^{n} b^{n}$ is the abstract kernel of many natural-language dependencies: the matching of a subject to its verb across an arbitrarily long centre-embedded clause ("the rat [that the cat [that the dog chased] killed] ate the malt") forces the same kind of unbounded counting that defeats any finite-state device, which is the structural reason generative grammar places natural language above the regular level 47.01.04.

Connections Master

Formal language theory 47.01.05. The phrase-structure grammars used here are context-free grammars in the sense of computer science; the pumping-lemma separations that pin down the Chomsky hierarchy are proved there.
Semantics and pragmatics 51.05.01. The syntactic tree is the input to compositional interpretation: each node receives a denotation built from its children, so the constituency decided here fixes the predictions of any semantic theory.
Phonology 51.02.01. Phonological rules apply to syntactically defined domains (the prosodic word, the phonological phrase), so constituency constrains where phonology can insert or delete material.
Philosophy of language 20.12.01. The competence–performance distinction and the autonomy thesis are continuous with the philosophical debate over whether grammar is a cognitive module, addressed in the foundations of philosophy of language.

Historical & philosophical context Master

Modern syntactic theory begins with Chomsky's Syntactic Structures (1957), which argued that the then-dominant finite-state and Markov models of language could not generate English and proposed transformational grammar in their place ^{[Chomsky 1957]}. The Aspects of the Theory of Syntax (1965) fixed the standard model: a base component of phrase-structure rules generating deep structures, a transformational component mapping deep to surface structure, and the competence–performance distinction that licensed the idealisation of a speaker-hearer ^{[Chomsky 1965]}. X-bar theory, the lexicon-centric model, and the successive constraints on movement (the A/A-bar, binding, and bounding theories of Government-and-Binding) occupied the 1970s and 1980s.

The Minimalist Program (1995) asked how much of that machinery is forced, reducing the computational system to Merge and Agree and shifting cross-linguistic variation onto the feature content of functional heads ^{[Chomsky 1995]}. The program is avowedly a research programme, not a finished theory: its value is the explanatory burden it places on any postulated operation.

The autonomy of syntax has never gone uncontested. Construction Grammar (Fillmore, Kay; Goldberg 1995), Cognitive Grammar (Langacker), and the usage-based work of Tomasello hold that grammatical structure emerges from a network of meaningful constructions and the statistics of use, denying a clean form/meaning border. The two positions coexist as a live empirical dispute: the generative side points to structure-dependent operations that hold across speakers regardless of meaning or frequency; the constructional side points to the semantic load of argument-structure patterns and to graded, frequency-sensitive judgements. Pedagogically, the field is best taught with both positions on the table, and that is how this unit is organised.

Bibliography Master

@book{Chomsky1957,
  author = {Chomsky, Noam},
  title = {Syntactic Structures},
  publisher = {Mouton},
  year = {1957},
}

@book{Chomsky1965,
  author = {Chomsky, Noam},
  title = {Aspects of the Theory of Syntax},
  publisher = {MIT Press},
  year = {1965},
}

@book{Chomsky1995,
  author = {Chomsky, Noam},
  title = {The Minimalist Program},
  publisher = {MIT Press},
  year = {1995},
}

@book{Carnie2013,
  author = {Carnie, Andrew},
  title = {Syntax: A Generative Introduction},
  edition = {4},
  publisher = {Wiley-Blackwell},
  year = {2013},
}

@book{Tallerman2015,
  author = {Tallerman, Maggie},
  title = {Understanding Syntax},
  edition = {4},
  publisher = {Routledge},
  year = {2015},
}

@book{Goldberg1995,
  author = {Goldberg, Adele},
  title = {Constructions: A Construction Grammar Approach to Argument Structure},
  publisher = {University of Chicago Press},
  year = {1995},
}

@book{HopcroftUllman2001,
  author = {Hopcroft, John E. and Motwani, Rajeev and Ullman, Jeffrey D.},
  title = {Introduction to Automata Theory, Languages, and Computation},
  edition = {2},
  publisher = {Addison-Wesley},
  year = {2001},
}

Prerequisites

51.01.01

Tier anchors

beginner: Carnie 2013 Syntax (Wiley-Blackwell) Ch. 1–3 (plain English); Tallerman 2015 Understanding Syntax (Routledge)
intermediate: Carnie 2013 Syntax (Wiley-Blackwell); Tallerman 2015 Understanding Syntax (Routledge) — phrase structure rules and trees
master: Chomsky 1957 Syntactic Structures (Mouton); Chomsky 1965 Aspects of the Theory of Syntax (MIT Press); Chomsky 1995 The Minimalist Program (MIT Press); Carnie 2013 Syntax

References

Chomsky — Syntactic Structures · Chomsky, N. (1957). Transformational analysis; the demonstration that phrase-structure grammars undergenerate English. Mouton.
Chomsky — Aspects of the Theory of Syntax · Chomsky, N. (1965). X-bar-style base components, transformations, and the competence/performance distinction. MIT Press.
Chomsky — The Minimalist Program · Chomsky, N. (1995). Merge, Agree, and the economy principles of the computational system. MIT Press.
Carnie — Syntax: A Generative Introduction · Carnie, A. (2013). Constituent structure, phrase-structure rules, X-bar theory, and movement. Wiley-Blackwell.
Tallerman — Understanding Syntax · Tallerman, M. (2015). Constituent vs dependency analyses; cross-linguistic argument structure. Routledge.
Goldberg — Constructions: A Construction Grammar Approach · Goldberg, A. (1995). Constructions as form-meaning pairings; the non-autonomy thesis. University of Chicago Press.
Hopcroft, Motwani & Ullman — Introduction to Automata Theory · Hopcroft, Motwani & Ullman (2001). The Chomsky hierarchy: regular, context-free, context-sensitive, recursively enumerable. Addison-Wesley.

Estimated time

beginner: 15m
intermediate: 40m
master: 85m