Projections, X-bar, Theta, and Case Theories

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Projection Principle

Projections are used to analyze the structure of phrases. X-bar theory is a theory of phrase structure in natural language. It considers word order and constituent structure, emphasizing the strict categorization between verbs and nouns, which is generalized to other phrasal categories, including sentences. Each phrasal category (e.g., NP) has a similar internal structure, allowing the same rules to apply to all categories. X-bar theory uses cross-categorial generalizations.

When we discuss the structure of a phrase, we are referring to the relationships between syntactic categories from left to right within the phrase. Projections connect or link all constituents in the phrase structure, based on certain common features of phrases. For example, every phrase contains a head (e.g., N, V, P), and the category of the phrase is the same type as the category of the head. Thus, if the head is N, the phrase is NP, and if the head is V, the phrase is VP, and so on.

The concept of the head is crucial in X-bar theory, as each head must be represented at all levels of analysis, including D-structure, S-structure, and logical form. This is known as the Projection Principle, ensuring that heads occur at the D-structure, even if they may not have a physical realization. If a position in the D-structure is empty, nothing can project from there to the S-structure. If the empty slot is the subject position of a sentence, a pleonastic element (e.g., "it," "there") will occur at the S-structure. These pleonastic elements are merely placeholders that are not base-generated.

The uniformity assumption posits that within a given language, the left-to-right ordering of constituents within categories is consistent (e.g., heads always precede complements). The head is the only obligatory category in a phrase, and other words modify it. The head determines the structure of the words or phrases adjacent to it. For example, a noun head in a noun phrase may not be directly modified by an adverb—only determiners, numerals, adjectives, etc., can pre-modify a noun head. Similarly, adjective heads cannot be premodified by nouns, due to the lexical properties of each head in a phrase.

Some heads take complements, and the relationship between a head and its complement is characterized by the fact that they are sisters, each c-commanding the other and being immediately dominated by the same node. X-bar theory proposes that all phrases have a consistent structure, called the X1 schema, which includes maximal projections and intermediate projections, with Xmax as a maximal projection and X1 as an intermediate projection. Each lexical category projects its own phrasal category; for example, N projects NP, V projects VP, Adv. projects Adv. P, and P projects PP.

In summary, X-bar theory provides a framework for understanding the structure of phrases in natural language, emphasizing the hierarchical relationships between heads, complements, specifiers, and adjuncts, as well as the uniformity of phrase structure within a language.

Theta Theory (θ-Theory)

Theta theory explains how syntactic structure determines the assignment of theta roles to constituents in a sentence. Theta roles are assigned to the arguments of a verb, such as the subject and object, indicating their thematic roles in the sentence. The subject is assigned the external theta role, while the object is assigned the internal theta role. The relationship between the external and internal arguments is called argument structure. Theta roles include Agent, Patient, Source, Instrument, Goal, Locative, Theme, Benefactive, and Experiencer, reflecting the different roles entities can play in a sentence.

Case Theory

Case theory deals with the assignment of abstract case to noun phrases in a sentence. Some languages have overt case marking systems, while others, like English, have less overt or restricted case marking. Abstract case is assigned to noun phrases based on their syntactic position and relationship to the verb. For example, the nominative case is assigned to the subject of a sentence, while the accusative case is assigned to the direct object. Case assignment follows syntactic principles, such as government theory and adjacency, ensuring that each noun phrase is marked for case and that lexical noun phrases are marked only once. Case theory helps explain how syntactic structure influences the assignment of case in natural language.

Some languages have overt case marking systems, while others, like English, have less overt or restricted case marking. In languages with extensive morphological case systems, every noun phrase (NP) in a sentence bears a particular relation to particular arguments. In contrast, in languages without such overt case marking systems, the assignment of case is more abstract and is determined by the syntactic structure of the sentence.

The Case Uniqueness Principle is a condition on syntactic representations, ensuring that every NP in a structure must be assigned a case, and that a lexical NP can be case-marked only once. This principle functions as a filter to exclude ill-formed structures that violate the case filter. Case assigners, such as lexical heads (e.g., N, V, P), assign abstract cases to noun phrases based on their syntactic relationships.

Case theory also distinguishes between different types of cases, such as nominative and accusative. Nominative case is assigned to noun phrases in subject positions, while accusative case is assigned to noun phrases in object positions. The verb in a sentence governs the assignment of accusative case to its object, but does not assign nominative case directly. Instead, nominative case is assigned by another element, often referred to as "Tense," in the verb.

In a syntactic theory of case assignment, the conditions under which cases are assigned must be syntactic. For example, in the assignment of accusative case, several different syntactic relations uniquely identify the noun phrase as the object of the verb, including linear adjacency, domination by the node that immediately dominates the case assigner, and domination by the lowest maximal projection that dominates the case assigner.

Conclusion 

In conclusion, case theory is concerned with the assignment of abstract case to noun phrases based on their syntactic positions and relationships within a sentence. It provides a framework for understanding how syntactic structure determines the assignment of case in different languages.