How to Draw X-bar Trees: Complements vs Adjuncts Explained

In X-bar syntax, functional categories are restructured so that determiners (D) are heads of determiner phrases (DP) with noun phrases as complements, complementizers (C) are obligatory heads of complementizer phrases (CP) with tense phrases as complements, and tense markers (T) are heads of tense phrases (TP) with subjects as specifiers and verb phrases as complements; these categories operate through specifier, adjunct, and complement rules where adjuncts repeat bar levels and complements are sisters to heads.

The inflectional phrase (IP/Tense Phrase) anchors events in time, containing tense, aspect, and modality markers. Greek and English share hierarchical structures despite different surface forms. The subject occupies the TP specifier; word order depends on whether verbs move past it. The determiner phrase (DP) anchors nouns in discourse, containing articles, demonstratives, and quantifiers. Greek allows determiners and articles to co-occur (unlike English), revealing different syntactic architectures. The complementizer phrase (CP) enables subordination and creates clause types beyond declaratives. Wh-words move to the front because they occupy the left periphery above TP. Biblical Hebrew's wayyiqtol and wayyaktal verb forms cannot be subordinated, indicating they've moved from V to C position, occupying the same slot as complementizers. This explains their unique behavior and demonstrates how syntactic positions distinguish verb forms.

This lecture extends X'-Bar theory by introducing Determiner Phrases (DP) and Tense Phrases (TP) as maximal projections, addressing limitations in the original specifier rule. In DP structure, the determiner projects as a phrase with a possessive in the specifier position and the noun as a complement, which properly captures C-command relations for binding theory (e.g., 'Selleck's book about himself' requires the DP to C-command the reflexive pronoun). Similarly, TP structure places the subject in the specifier position of T', with the T head containing tense information and the VP as a complement, replacing the trinary branching TP rule from phrase structure grammar with a binary X'-Bar structure.

In phrase structure grammar, a sentence is analyzed as a Tense Phrase (TP) consisting of a Noun Phrase (NP) and a Verb Phrase (VP); when modal or auxiliary verbs are present, the TP includes a T category (Tense marker); additionally, Complementizer Phrases (CP) introduced by words like 'that', 'if', or 'whether' consist of a complementizer plus a TP, and can occupy either the VP or NP position in a sentence, with the 'that' complementizer being optionally deletable.

VPs can have multiple adjuncts, each sister to Vbar and daughter of another Vbar. NP projection with determiners: determiners are specifiers, sister to Nbar and daughter of NP. TP projection with embedded clauses: embedded clause (TP) is complement of verb, sister to V and daughter of Vbar, projects through Tbar to TP. CP with complementizer: complementizer is head, embedded clause is TP complement, presented by C. Main clause TP: subject is specifier, tense projects to Tbar, VP projects to Vbar, CP is complement of verb.

Movement in X-bar theory is a syntactic process where elements move to satisfy morphological and syntactic requirements: morphological movement occurs when defective heads (like tense inflections) move to attach to verbs, while syntactic movement ensures subjects appear before predicates, questions require inversion, and WH-phrases move to the specifier of C position.

Two theoretical approaches explain what happens during movement: (1) Copy theory suggests the moved element leaves behind a copy, creating a chain of copies where only the highest copy is pronounced; (2) Trace theory proposes that movement leaves behind an unpronounced trace category (marked with a subscript matching the moved element). These theories make different empirical predictions but are often treated as equivalent for many purposes.

The copy theory of movement proposes that syntactic movement is actually another instance of merge, where a phrase is merged into the tree more than once. When something moves, it creates multiple copies in different positions. For example, in wh-movement, 'what' appears in both its original position and its new position. This explains reconstruction phenomena where moved elements can be interpreted as if they were still in their original position. The theory suggests that syntax hands phonology and semantics representations with multiple copies, and these systems must choose which copy to pronounce or interpret.

The general x-bar format applies universally: XP rewrites as Specifier + X-bar; X-bar rewrites as Head + Complement. This single format accounts for NP, VP, PP, and CP structures. The inflection phrase (IP) is headed by an auxiliary with VP as complement. The VP internal subject hypothesis proposes subjects originate in VP specifier and move to IP specifier, explaining subject-verb agreement. Wh-words move to IP specifier position. This movement creates traces showing original positions. The VP projects from V-bar to VP, with V-bar optionally having NP complement for transitive verbs.

X-bar theory cannot generate certain word orders found in natural languages, such as VSO order in Irish where the subject intervenes between the verb and object. To address this, linguists propose movement rules—transformational rules that transform one tree structure into another. The first such rule examined is V-to-T movement (head-to-head movement), which explains how elements can change position while maintaining grammatical structure. This mechanism accounts for word order paradoxes where surface order contradicts X-bar predictions but has other linguistic evidence supporting it.

Binding Theory in syntax consists of three principles governing coreference: Principle A requires anaphors (reflexives like 'themselves') to be bound within their binding domain (the smallest TP containing them); Principle B requires pronouns to be free within their binding domain (not bound by any antecedent inside it); and Principle C states that reflexive expressions must be free (cannot be co-indexed with anything). The binding domain is the smallest TP containing the NP being analyzed, and binding relationships are established before syntactic movement occurs.

In VSO languages like Scottish Gaelic, two hypotheses compete: flat structure (NPs as verb sisters) versus hierarchical structure (subject higher than object). Binding theory distinguishes them through anaphor distribution. In flat structures with symmetric c-command, either NP could be an anaphor. In hierarchical structures, only the lower NP can be anaphor since the higher NP c-commands it. Scottish Gaelic data confirms the hierarchical hypothesis: anaphors appear only in object position, not subject position. This demonstrates how binding facts reveal hidden hierarchical levels despite surface word order, showing that syntax reveals underlying structure beyond surface appearance.

Binding Theory consists of three principles governing how expressions interact: (1) Principle A: Anaphors must be bound locally within their clause - the antecedent must command the anaphor and they must be co-indexed. This explains why 'João se vestiu' works but 'João disse que si mesmo fez o bolo' fails (antecedent in different clause). (2) Principle B: Pronouns must be free within their clause - they cannot be co-indexed with an antecedent in the same clause. This explains why 'João o vestiu' fails but 'Nós fizemos o bolo' works (pronome can refer outside). (3) Principle C: Referential expressions are always free and never depend on anything else. This explains why 'João beijou a Maria' requires 'João' and 'Maria' to be different entities. These principles explain intuitive grammatical judgments across all human languages.

Binding Theory in syntax establishes three principles governing coreference: (1) Anaphors (like 'himself') must be bound within their binding domain (the same clause as their antecedent); (2) Pronouns (like 'her') must be free within their binding domain; (3) Reflexives (like 'herself') must be free everywhere in the sentence. These principles determine grammaticality through co-indexation and c-command relationships between elements.

Anaphors (reflexive pronouns like 'himself') require local antecedents within their c-command domain, while regular pronouns exclude local antecedents. In complex sentences like 'The witness who saw the thief recognizes himself,' 'himself' cannot refer to 'the thief' even though 'the thief' is linearly closer, because 'the thief' does not c-command 'himself.' This inversion in binding relations demonstrates that binding is determined by hierarchical structure, not linear proximity.

This section develops the X-bar theory framework and demonstrates its application to cross-linguistic analysis. The instructor presents three universal rules governing syntactic structure: adjuncts, specifiers, and complements must each be sister to X0-bar dominated by X-bar. Using Tokish as a case study, the instructor shows how the same theoretical framework can account for different languages by modifying parameter settings. In English, the complement follows the head ('read the book'), while in Tokish, the complement precedes the head ('u do key tab'). The instructor emphasizes that English is morphologically poor (no case marking), unlike languages like Arabic and Turkish where word forms change based on grammatical function.

This section covers three major parameters explaining cross-linguistic variation. The Q-Parameter classifies languages by whether they allow wh-movement to the sentence beginning (English and Spanish allow it, Chinese does not). The Head-First/Head-Last Parameter classifies languages by head position in phrases (English is head-initial, Korean is head-final, German shows variation). The Prominence of Concordance vs Information Structure parameter explains languages that emphasize subject-verb agreement (English) versus those that emphasize topic and focus (Japanese). Spanish is described as 'conspiratorial' because it shows both properties.

X-bar theory explains cross-linguistic variation in word order through three parameterized rules: specifier placement (before or after the head), adjunct placement (before or after the head), and complement placement (before or after the head). In English, specifiers must appear before the head, adjuncts can appear on either side, and complements must appear after the head. Children acquire their native language by setting these three parameters through exposure to parental speech, explaining why they can quickly learn complex syntactic structures despite limited cognitive resources.

Three key parameters explain cross-linguistic variation in syntactic structure. The Head Position Parameter determines whether heads appear at beginning or end position (English: head-first; Urdu/Hindi: head-last). The WH Parameter governs question word placement (English requires initial position; other languages allow final position). The Null Subject Parameter determines subject obligatoriness (English requires filled subjects; Urdu/Hindi allows null subjects). These parameters represent binary choices that children acquire when learning their native language, demonstrating how universal principles interact with language-specific settings to produce the diversity observed across human languages.

English follows head-initial right-branching structure (main clause first, then additional information). Chinese follows head-final left-branching structure, where descriptive information comes before the main clause. For example, in English: 'I want to read the book that my friend bought me when he went to Tokyo.' In Chinese: 'I want to read last week my friend in Tokyo time for me bought book.' The verb order remains subject-verb-object.