Within the Government and Binding (GB) and minimalist ap- proaches to syntactic theory, NPs are licensed by structural Case, which is assigned under a local version of c-command (government; see section 4.3) by some particular node. This is one of the primary motivations for Aoun and Sportiche to introduce m-command. Nom- inative case is assigned by InX in the conWguration in (34a); genitive case, by a noun in the conWguration in (34b). () (a) IP (b) NP NP I Ј NP N Ј NOM Infl VP GEN N PP If Case licensing does indeed occur under a c-command-like structural relation, then clearly m-command is most appropriate. In the trees in (34) the case assigning node m-commands—but does not c-command— the NP it assigns case to. 4.2.5 Barker and Pullum: A unified approach to command relations Barker and Pullum (1990)12 ; 13 oVer an important contribution to our understanding of command relations and their underlying similarities and diVerences. They observe that many of the deWnitions like those given above of command are vague and imprecise (such as what precisely is meant by ‘‘Wrst’’ in Wrst branching node). They provide a uniWed account of all command relationships, and precise typology of the various kinds of command relationships. Barker and Pullum deWne all command relationships in terms of various kinds of ‘‘upper bounds’’ in terms of various relationships or properties.14 12 For a detailed discussion of the mathematical properties of Barker and Pullum’s proposal, see Kracht (1993). 13 In addition, Barker and Pullum also observe a number of formal properties of command relations, including the interrelationships between various kinds of command. See the original work for details. 14 Note that Barker and Pullum’s deWnitions do not include the neither/nor condition discussed in section 4.5.3. They claim to see no empirical reason for it. They do not discuss the i-within-i facts. It is a relatively minor change to Wx their deWnitions so that it includes this condition. 60 preliminaries (35) The set of upper bounds for a with respect to a property P (writ- ten UB(a, P)) is given by UB(a, P) ¼ {b j b / þ a & P(b) } That is, some node b is an upper bound for a,ifb properly dominates a, and satisWes property P. Most command relationships actually refer to the minimal upper bounds (MUB): (36) MUB(a, P) ¼{bj b 2 UB(a, P) & 8x[(x2 UB(a, P) & b /*x) ! (b ¼ x)] } (This is an antisymmetricity requirement: b is a minimal upper bound for a if b is an upper bound for a satisfying P, and if for all nodes x that are upper bounds for a,ifb (reXexively) dominates x, then b is identical to x.) As such, command relations will be deWned in terms of types of relationships between that node and some (minimal) dominator of that node. Command relations are deWned as pairs of nodes, both of which are dominated by the same upper bounds relative to some property P: (37)C P ¼ { <a, b>: 8x [(x 2 MUB(a, P)) ! x /*b]} The command domain of some node a is the set of nodes with which it is paired, relative to some MUB as deWned by property P. What is left to deWne is the nature of the property P. This will vary depending upon the type of command relationship that is involved. Langacker’s command is deWned in terms of S nodes. So the deWning relation is: (38) S-command is the command relation C P1 , where P1 is given by: P1 ¼ {a j label(a) ¼ S} Although no one has ever limited command to the NP node, Barker and Pullum state the equivalent relation deWned in terms of NPs for completeness sake: (39) NP-command is the command relation C P2 ,whereP2 is given by: P2 ¼ {a j label(a) ¼ NP} Lasnik’s kommand is the combination of S-command and NP-command: (40) K-command is the command relation C P3 , where P3 is given by: P3 ¼ {a j label(a) 2 {S, NP} } M-command (Barker and Pullum’s max-command) assumes the existence of the set max, which is the set of XP categories. c-command and government 61 (41) M-command is the command relation C P4 , where P4 is given by: P4 ¼ {a j label(a) 2 max} Reinhart’s original deWnition of c-command referenced branching nodes, rather than labeled nodes. Barker and Pullum’s deWnition of branching is rather involved. In order to describe branching, one has to reference a treelet—that is, a structure consisting of a mother node and at least two distinct daughters. The mother in this treelet does not have to be the immediate dominator of the c-commanding node, but it does have to reference immediate domination in order to establish the branching relation. Barker and Pullum’s deWnition of immediate dominance (M for mothership) is given in (42): (42)M¼ {<a, b> j (a /*b)&:9x[a/*x/*b]} (a dominates b, and there is no node x, such that a dominates x and x dominates b). Branching is deWned in the relation P5, where the dominator must be the mother of two distinct nodes: (43) C-command is the command relation C P5 , where P5 is given by: P5 ¼ {a j:9xy [x 6¼ y & M(a, x) & M(a, y)]} Note that neither x nor y here must be the c-commander or c-commandee. The node a need not immediately dominate these nodes (although it must dominate them), however, a must immedi- ately dominate x and y, which themselves dominate (potentially reXex- ively) the c-commander and the c-commandee. Note, however, that while c-command is frequently deWned in terms of branching nodes, most scholars do not, in practice, require binary (or n-ary) branching. This intuition is captured in the informal deWnition of c-command given in section 4.2.1. Barker and Pullum provide an alternative deWnition based on dom- inating node, not necessarily branching ones. This is the relationship that Emonds calls ‘‘minimal c-command’’, and is actually the most frequent usage in the literature (although it is the least common deWnition). Barker and Pullum call this IDC-command (immediate dominance c-command). (44) IDC-command is the command relation C P6 ,whereP6 is given by: P6 ¼ N (N the set of nodes) This corresponds to our deWnition in (23). 62 preliminaries 4.3 Government In Chapter 1, we provided local or immediate variants of the structural relations of precedence and dominance. One interpretation of the term ‘‘government’’ provides the local variant of c-command. Government, unsurprisingly, was the central notion in the Government and Binding (GB) framework (Chomsky 1981). It was perhaps the most important structural relation in that theory until the paradigm shift in Chomsk- yan linguistics known as the Minimalist Program (MP), which started in the early 1990s (however, a relation very similar to government has re-emerged in the Phase-theoretic version of minimalism (Chomsky 2000, 2001, 2004a, b)). Somewhat confusingly, the term ‘‘govern’’ really has two quite dis- tinct usages in GB theory. The Wrst usage is as a structural relation (essentially local c-command), the second usage is as a licensing condition. In GB theory, all the nodes in a tree must be licensed in order to surface. Licensing occurs when the licensor stands in a gov- ernment relationship to the element needing licensing. For example, an NP is licensed with Accusative Case, when it stands in a government relationship with a tensed transitive verb (the licensor). In the GB literature, the term ‘‘government’’ is thus used in two distinct (but interrelated ways). We will be concerned here only with the struct- ural relation usage, although the licensing relationships deWned using the structural relation serve as the primary evidence for the approach. There are many deWnitions of government. I give a typical, but partly incomplete deWnition: (45) Government: A governs B iV a) A c-commands B; b) There is no X, such that A c-commands X and X c-commands B. The workings of this deWnition can be seen in the trees in (46). () (a) D b) D AC AC BE XE BF c-command and government 63 A governs B in (46a) but not in (46b). The node X intervenes blocking A’s government of B. The relevant question, of course, is what X is. X can vary depending upon the type of licensing relationship. This is the ‘‘minimality’’ approach to government (see Rizzi 1989); in earlier versions of government, condition (b) of the deWnition was given in terms of intervening ‘‘barrier’’ nodes, rather than intervening potential c-commanders. The barrier nodes dominated the c-com- manded node rather than c-commanded it. The diVerence between the two has to do with whether a head can govern into the speciWer of its complement (these notions will be explained in Ch. 7; for a textbook treatment of such deWnitions, see ch. 2 of Haegeman or, for a more formal deWnition, see Chomsky 1981). In early versions of GB theory, X was usually deWned as either a lexical head (giving the licensing relationships known variously as head government, lexical government or theta government, depending on the particular restrictions on X) or a co-indexed antecedent element (known as antecedent government). Rizzi (1989) proposed that, for Wller–gap dependencies (movement relationships) at least, the nature of X was relativized to the type of relationship that held between the Wller and the gap or trace. If the Wller and the gap were both heads, then X would be a head. If the Wller and the gap were related by an argument relationship (i.e. A-movement, such as NP raising) then X would be an argument, and if the Wller and gap were related by an A-bar chain, (such as wh-movement), then X is another A-bar element. For a survey of the function of the government relation, see any good GB theory textbook (such as Haegeman 1994 or Cowper 1992). For a discussion of the formal properties of this relation (and how it is technically not a c-command relation, narrowly construed) see Barker and Pullum (1990).15 15 Their argument is as follows. They start with the assumption that all c-command relationships have the property of ‘‘descent’’. That is, if a commands b then a commands b’s descendants. Government by deWnition lacks this property, so according to Barker and Pullum it is not really a command relationship. It seems to me that this is a matter of terminology. The deWnitions of immediate relations (e.g. immediate domination) have related properties. That is, if A immediately precedes B, then it does not immediately precede B’s followers (although it does precede them). We would not want to say that ‘‘immediate’’ precedence is ‘‘really’’ precedence, just because it is not transitive; nor should we say that government is not a command relation because it is deWned to be a local relation, and does not obey descent. We just need to distinguish between the general relation and the local one. We should also note that descent is a problem for any system (like Chomsky’s Phase theory) that is strongly cyclic, since nodes in such a system are not allowed to c-command into lower cycles. 64 preliminaries 4.4 Concluding remarks The relations of c-command and government, taken together with the varieties of precedence and dominance discussed in the last chapter, provide us with mechanisms for describing constituent structure in some detail. We have not yet, however, discussed the ways constituent structure might be constructed. Nor have we really discussed what kinds of information constituent structures represent. In the next chapter we turn to one simple mechanism for deriving constituent structures, namely, phrase structure grammars, and begin an investi- gation of what types of information are encoded in these structures. c-command and government 65 This page intentionally left blank Part 2 Phrase Structure Grammars and X-bar Theory This page intentionally left blank 5 Capturing Constituent Structure: Phrase Structure Grammars 5.1 Before the Chomskyan revolution: Conflating semantic and structural relations The analysis of sentences as structured entities is a very old idea. The discipline of pure logic is based on this intuition. Logic distinguishes between predicates (properties and the relations between entities) and arguments (the participants in the predicate relations). Since predicates and arguments can be represented by strings of words, it follows that a basic notion of constituency can be found in this semantic distinction. We can trace this at least as far back as Apollonius Dyscolus (c. ad 200), and probably much earlier to Aristotle. This idea—that sentential units are deWned according to their se- mantic function—is perhaps one of the most enduring concepts in syntactic analysis. Indeed, today we can observe modern syntactic equivalents of such analyses in the form of dependency or categorial grammars (see Ch. 9). Students learning grammar at schools through- out the Americas are trained to identify constituents according to their semantic function as ‘‘subjects’’, ‘‘predicates’’, or ‘‘modiWers’’. In both the European and American Structuralist traditions of the late nineteenth and early twentieth century, we Wnd similar notions. For example, Saussure (1910; Eng. trans. 1959) discusses syntagmatic relations (which amount to semantically deWned relations among words and linear strings of words). Perhaps the most inXuential analysis of constituency in this tradition1 was BloomWeld (1933). BloomWeld proposed a system for analyzing sentences into their composite parts 1 I leave aside the lexical bar-notation tradition of Z. Harris (1951), which we will return to in the chapter on X-bar theory. . c-command-like structural relation, then clearly m-command is most appropriate. In the trees in (34) the case assigning node m-commands—but does not c-command—. another A-bar element. For a survey of the function of the government relation, see any good GB theory textbook (such as Haegeman 199 4 or Cowper 199 2). For