Harris's grammar

Harris distinguished within the total set of grammatical sentences in a particular language (for example, English) two complementary subsets: kernel sentences (the set of kernel sentences being described as the kernel of the grammar) and nonkernel sentences. The difference between these two subsets lies in nonkernel sentences being derived from kernel sentences by means of transformational rules. For example, “The workers rejected the ultimatum” is a kernel sentence that may be transformed into the nonkernel sentences “The ultimatum was rejected by the workers” or “Did the workers reject the ultimatum?” Each of these may be described as a transform of the kernel sentence from which it is derived. The transformational relationship between corresponding active and passive sentences (e.g., “The workers rejected the ultimatum” and “The ultimatum was rejected by the workers”) is conventionally symbolized by the rule N₁ V N₂ → N₂ be V + en by N₁, in which N stands for any noun or noun phrase, V for any transitive verb, en for the past participle morpheme, and the arrow (→) instructs one to rewrite the construction to its left as the construction to the right. (There has been some simplification of the rule as it was formulated by Harris.) This rule may be taken as typical of the whole class of transformational rules in Harris's system: it rearranges constituents (what was the first nominal, or noun, N₁, in the kernel sentence is moved to the end of the transform, and what was the second nominal, N₂, in the kernel sentence is moved to initial position in the transform), and it adds various elements in specified positions (be, en, and by). Other operations carried out by transformational rules include the deletion of constituents; e.g., the entire phrase “by the workers” is removed from the sentence “The ultimatum was rejected by the workers” by a rule symbolized as N₂ be V+en by N₁ → N₂ be V+en. This transforms the construction on the left side of the arrow (which resulted from the passive transformation) by dropping the by-phrase, thus producing “The ultimatum was rejected.”

Chomsky's grammar

Chomsky's system of transformational grammar, though it was developed on the basis of his work with Harris, differs from Harris's in a number of respects. It is Chomsky's system that has attracted the most attention and has received the most extensive exemplification and further development. As outlined in Syntactic Structures (1957), it comprised three sections, or components: the phrase-structure component, the transformational component, and the morphophonemic component. Each of these components consisted of a set of rules operating upon a certain “input” to yield a certain “output.” The notion of phrase structure may be dealt with independently of its incorporation in the larger system. In the following system of rules, S stands for Sentence, NP for Noun Phrase, VP for Verb Phrase, Det for Determiner, Aux for Auxiliary (verb), N for Noun, and V for Verb stem.

1. SNP+VP

2. VPVerb+ NP

3. NP Det +N

4. Verb Aux +V

5. Detthe, a…

6. Nman, ball…

7. Auxwill, can

8. V hit, see…

This is a simple phrase-structure grammar. It generates and thereby defines as grammatical such sentences as “The man will hit the ball,” and it assigns to each sentence that it generates a structural description. The kind of structural description assigned by a phrase-structure grammar is, in fact, a constituent structure analysis of the sentence.

Figure 1

V P

Verb NP

In these rules, the arrow can be interpreted as an instruction to rewrite (this is to be taken as a technical term) whatever symbol appears to the left of the arrow as the symbol or string of symbols that appears to the right of the arrow. For example, rule (2) rewrites the symbol VP as the string of symbols Verb + NP, and it thereby defines Verb + NP to be a construction of the type VP. Or, alternatively and equivalently, it says that constructions of the type VP may have as their immediate constituents constructions of the type Verb and NP (combined in that order). Rule (2) can be thought of as creating or being associated with the tree structure. Rules (1)–(8) do not operate in isolation but constitute an integrated system. The symbol S (standing mnemonically for “sentence”) is designated as the initial symbol. This information is not given in the rules (1)–(8), but it can be assumed either that it is given in a kind of protocol statement preceding the grammatical rules or that there is a universal convention according to which S is always the initial symbol. It is necessary to begin with a rule that has the initial symbol on the left. Thereafter any rule may be applied in any order until no further rule is applicable; in doing so, a derivation can be constructed of one of the sentences generated by the grammar. If the rules are applied in the following order: (1), (2), (3), (3), (4), (5), (5), (6), (6), (7), (8), then assuming that “the” is selected on both applications of (5), “man” on one application of (6), and “ball” on the other, “will” on the application of (7), and “hit” on the application of (8), the following derivation of the sentence “The man will hit the ball” will have been constructed:

1. S

2. NP+VP by rule (1)

3. NP+ Verb +NP by rule (2)

4. Det+ N + Verb +NP by rule (3)

5. Det+ N + Verb +Det + N by rule (3)

6. Det+ N + Aux+V +Det +N by rule (4)

7. the+ N+ Aux+V +Det + N by rule (5)

8. the+ N+ Aux+V +the +N by rule (5)

9. the+ man + Aux+V +the +N by rule (6)

10. the+ man + Aux+V +the +ball by rule (6)

11. the+ man + will +V +the +ball by rule (7)

12. the+ man + will +hit +the +ball by rule (8)

Many other derivations of this sentence are possible, depending on the order in which the rules are applied. The important point is that all these different derivations are equivalent in that they can be reduced to the same tree diagram. If this is compared with the system of rules, it will be seen that each application of each rule creates or is associated with a portion (or subtree) of the tree. The tree diagram, or phrase marker, may now be considered as a structural description of the sentence “The man hit the ball.” It is a description of the constituent structure, or phrase structure, of the sentence, and it is assigned by the rules that generate the sentence.

Figure 2

S

NP VP

Det N Verb NP²

Det N

The man Aux. V

will hit the ball

It is important to interpret the term generate in a static, rather than a dynamic, sense. The statement that the grammar generates a particular sentence means that the sentence is one of the totality of sentences that the grammar defines to be grammatical or well formed. All the sentences are generated, as it were, simultaneously. The notion of generation must be interpreted as would be a mathematical formula containing variables. For example, in evaluating the formula y ² + y for different values of y, one does not say that the formula itself generates these various resultant values (2, when y = 1; 5, when y = 2; etc.) one after another or at different times; one says that the formula generates them all simultaneously or, better still perhaps, timelessly. The situation is similar for a generative grammar. Although one sentence rather than another can be derived on some particular occasion by making one choice rather than another at particular places in the grammar, the grammar must be thought of as generating all sentences statically or timelessly.

It has been noted that, whereas a phrase-structure grammar is one that consists entirely of phrase-structure rules, a transformational grammar (as formalized by Chomsky) includes both phrase-structure and transformational rules (as well as morphophonemic rules). The transformational rules depend upon the prior application of the phrase-structure rules and have the effect of converting, or transforming, one phrase marker into another. What is meant by this statement may be clarified first with reference to a purely abstract and very simple transformational grammar, in which the letters stand for constituents of a sentence (and S stands for “sentence”):

PS rules

1. S → A+B

2. B → C+D

3. A → a+b

4. C → c+e+f

5. D → d+g+h

T rule

A+C+D → D+A

The first five rules are phrase-structure rules (PS rules); rule (6) is a transformational rule (T rule). The output of rules (1)–(5) is the terminal string a + b + c + e + f + d + g + h, which has associated with it the structural description indicated by the phrase marker. Rule (6) applies to this terminal string of the PS rules and the associated phrase marker. It has the effect of deleting C (and the constituents of C) and permuting A and D (together with their constituents). The result is the string of symbols d + g + h + a + b, with the associated phrase marker shown in Figure 3 (b).

Figure 3

S

A B

D

a b C d g h

c e f

Figure 3 b

S

D A

d g h a b

The phrase marker shown in Figure 3 may be described as underlying, and the phrase marker shown in Figure 3 b as derived with respect to rule (6). One of the principal characteristics of a transformational rule is its transformation of an underlying phrase marker into a derived phrase marker in this way. Transformational rules, in contrast with phrase-structure rules, are also formally more heterogeneous and may have more than one symbol on the left-hand side of the arrow. The linguistic importance of these abstract considerations may be explained with reference to the relationship that holds in English between active and passive sentences.

Chomsky's rule for relating active and passive sentences (as given in Syntactic Structures) is very similar, at first sight, to Harris's, discussed above. Chomsky's rule is: NP1 –Aux-V-NP2Aux+be+en-V-by+NP1

This rule, called the passive transformation, presupposes and depends upon the prior application of a set of phrase-structure rules. For simplicity, the passive transformation may first be considered in relation to the set of terminal strings generated by the phrase-structure rules (1)–(8) given earlier. The string “the + man + will + hit + the + ball” (with its associated phrase marker, as shown in (Figure 2) can be treated not as an actual sentence but as the structure underlying both the active sentence “The man will hit the ball” and the corresponding passive “The ball will be hit by the man.” The passive transformation is applicable under the condition that the underlying, or “input,” string is analyzable in terms of its phrase structure as NP - Aux - V - NP (the use of subscript numerals to distinguish the two NPs in the formulation of the rule is an informal device for indicating the operation of permutation). In the phrase marker in Figure 2 “the” + “man” are constituents of NP, “will” is a constituent of Aux, “hit” is a constituent of V, and “the” + “ball” are constituents of NP. The whole string is therefore analyzable in the appropriate sense, and the passive transformation converts it into the string “the + ball + will + be + en + hit + by + the + man.” A subsequent transformational rule will permute “en + hit” to yield “hit + en,” and one of the morphophonemic rules will then convert “hit + en” to “hit” (as “ride + en” will be converted to “ridden”; “open + en” to “opened,” and so on).

Every transformational rule has the effect of converting an underlying phrase marker into a derived phrase marker. The manner in which the transformational rules assign derived constituent structure to their input strings is one of the major theoretical problems in the formalization of transformational grammar. Here it can be assumed not only that “be + en” is attached to Aux and “by” to NP (as indicated by the plus signs in the rule as it has been formulated above) but also that the rest of the derived structure is as shown in Figure 4. The phrase marker in Figure 4 formalizes the fact, among others, that “the ball” is the subject of the passive sentence “The ball will be hit by the man,” whereas “the man” is the subject of the corresponding active “The man will hit the ball” (cf. Figure 2).

Figure 4

S

NP VP

Det N Verb NP²

by NP3

Det N

The ball Aux. V

will be en hit the man

Although the example above is a very simple one, and only a single transformational rule has been considered independently of other transformational rules in the same system, the passive transformation must operate, not only upon simple noun phrases like “the man” or “the ball,” but upon noun phrases that contain adjectives (“the old man”), modifying phrases (“the man in the corner”), relative clauses (“the man who checked in last night”), and so forth. The incorporation, or embedding, of these other structures with the noun phrase will be brought about by the prior application of other transformational rules. It should also be clear that the phrase-structure rules require extension to allow for the various forms of the verb (“is hitting,” “hit,” “was hitting,” “has hit,” “has been hitting,” etc.) and for the distinction of singular and plural.

It is important to note that, unlike Harris's, Chomsky's system of transformational grammar does not convert one sentence into another: the transformational rules operate upon the structures underlying sentences and not upon actual sentences. A further point is that even the simplest sentences (i.e., kernel sentences) require the application of at least some transformational rules. Corresponding active and passive sentences, affirmative and negative sentences, declarative and interrogative sentences, and so on are formally related by deriving them from the same underlying terminal string of the phrase-structure component. The difference between kernel sentences and nonkernel sentences in Syntactic Structures (in Chomsky's later system the category of kernel sentences is not given formal recognition at all) resides in the fact that kernel sentences are generated without the application of any optional transformations. Nonkernel sentences require the application of both optional and obligatory transformations, and they differ one from another in that a different selection of optional transformations is made.

Modifications in Chomsky's grammar

Chomsky's system of transformational grammar was substantially modified in 1965. Perhaps the most important modification was the incorporation, within the system, of a semantic component, in addition to the syntactic component and phonological component. (The phonological component may be thought of as replacing the morphophonemic component of Syntactic Structures.) The rules of the syntactic component generate the sentences of the language and assign to each not one but two structural analyses: a deep structure analysis as represented by the underlying phrase marker, and a surface structure analysis, as represented by the final derived phrase marker. The underlying phrase marker is assigned by rules of the base (roughly equivalent to the PS [Phrase-Structure] rules of the earlier system); the derived phrase marker is assigned by the transformational rules. The meaning of the sentence is derived (mainly, if not wholly) from the deep structure by means of the rules of semantic interpretation; the phonetic realization of the sentence is derived from its surface structure by means of the rules of the phonological component. The grammar (“grammar” is now to be understood as covering semantics and phonology, as well as syntax) is thus an integrated system of rules for relating the pronunciation of a sentence to its meaning. The syntax, and more particularly the base, is at the “heart” of the system, as it were: it is the base component (as the arrows in the diagram indicate) that generates the infinite class of structures underlying the well-formed sentences of a language. These structures are then given a semantic and phonetic “interpretation” by the other components.

Figure 5

Base component

Transformational component

Semantic component

The base consists of two parts: a set of categorial rules and a lexicon. Taken together, they fulfill a similar function to that fulfilled by the phrase-structure rules of the earlier system. But there are many differences of detail. Among the most important is that the lexicon (which may be thought of as a dictionary of the language cast in a particular form) lists, in principle, all the vocabulary words in the language and associates with each all the syntactic, semantic, and phonological information required for the correct operation of the rules. This information is represented in terms of what are called features. For example, the entry for “boy” might say that it has the syntactic features: [+ Noun], [+ Count], [+ Common], [+ Animate], and [+ Human]. The categorial rules generate a set of phrase markers that have in them, as it were, a number of “slots” to be filled with items from the lexicon. With each such “slot” there is associated a set of features that define the kind of item that can fill the “slot.” If a phrase marker is generated with a “slot” for the head of a noun phrase specified as requiring an animate noun (i.e., a noun having the feature [+ Animate]), the item “boy” would be recognized as being compatible with this specification and could be inserted in the “slot” by the rule of lexical substitution. Similarly, it could be inserted in “slots” specified as requiring a common noun, a human noun, or a countable noun, but it would be excluded from positions that require an abstract noun (e.g., “sincerity”) or an uncountable noun (e.g., “water”). By drawing upon the syntactic information coded in feature notation in the lexicon, the categorial rules might permit such sentences as “The boy died,” while excluding (and thereby defining as ungrammatical) such nonsentences as “The boy elapsed.”

One of the most controversial topics in the development of transformational grammar is the relationship between syntax and semantics. Scholars working in the field are now agreed that there is a considerable degree of interdependence between the two, and the problem is how to formalize this interdependence. One school of linguists, called generative semanticists, accept the general principles of transformational grammar but have challenged Chomsky's conception of deep structure as a separate and identifiable level of syntactic representation. In their opinion, the basic component of the grammar should consist of a set of rules for the generation of well-formed semantic representations. These would then be converted by a succession of transformational rules into strings of words with an assigned surface-structure syntactic analysis, there being no place in the passage from semantic representation to surface structure identifiable as Chomsky's deep structure. Chomsky himself has denied that there is any real difference between the two points of view and has maintained that the issue is purely one of notation. That this argument can be put forward by one party to the controversy and rejected by the other is perhaps a sufficient indication of the uncertainty of the evidence. Of greater importance than the overt issues, in so far as they are clear, is the fact that linguists are now studying much more intensively than they have in the past the complexities of the interdependence of syntax, on the one hand, and semantics and logic, on the other. Whether it will prove possible to handle all these complexities within a comprehensive generative grammar remains to be seen.

The role of the phonological component of a generative grammar of the type outlined by Chomsky is to assign a phonetic “interpretation” to the strings of words generated by the syntactic component. These strings of words are represented in a phonological notation (taken from the lexicon) and have been provided with a surface-structure analysis by the transformational rules. The phonological elements out of which the word forms are composed are segments consisting of what are referred to technically as distinctive features (following the usage of the Prague school, see below The Prague school). For example, the word form “man,” represented phonologically, is composed of three segments: the first consists of the features [+ consonantal], [+ bilabial], [+ nasal], etc.; the second of the features [+ vocalic], [+ front], [+ open], etc.; and the third of the features [+ consonantal], [+ alveolar], [+ nasal], etc. (These features should be taken as purely illustrative; there is some doubt about the definitive list of distinctive features.) Although these segments may be referred to as the “phonemes” /m/, /a/, and /n/, they should not be identified theoretically with units of the kind discussed in the section on Phonology under Structural linguistics. They are closer to what many American structural linguists called “morphophonemes” or the Prague school linguists labelled “archiphonemes,” being unspecified for any feature that is contextually redundant or predictable. For instance, the first segment of the phonological representation of “man” will not include the feature [+ voice]; because nasal consonants are always phonetically voiced in this position in English, the feature [+ voice] can be added to the phonetic specification by a rule of the phonological component.

One further important aspect of generative phonology (i.e., phonology carried out within the framework of an integrated generative grammar) should be mentioned: its dependence upon syntax. Most American structural phonologists made it a point of principle that the phonemic analysis of an utterance should be carried out without regard to its grammatical structure. This principle was controversial among American linguists and was not generally accepted outside America. Not only has the principle been rejected by the generative grammarians, but they have made the phonological description of a language much more dependent upon its syntactic analysis than has any other school of linguists. They have claimed, for example, that the phonological rules that assign different degrees of stress to the vowels in English words and phrases and alter the quality of the relatively unstressed vowel concomitantly must make reference to the derived constituent structure of sentences and not merely to the form class of the individual words or the places in which the word boundaries occur.

Tagmemics

The system of tagmemic analysis, as presented by Kenneth L. Pike, was developed for the analysis not only of language but of all of human behaviour that manifests the property of patterning. In the following treatment, only language will be discussed.

 

Modes of language

Every language is said to be trimodal—i.e., structured in three modes: phonology, grammar, and lexicon. These modes are interrelated but have a considerable degree of independence and must be described in their own terms. Phonology and lexicon should not be seen as mere appendages to grammar, the former simply specifying which phonemes can combine to form morphemes (or morphs), and the latter simply listing the morphemes and other meaningful units with a description of their meaning. There are levels of structure in each of the modes, and the units of one level are not necessarily coterminous with those of another. Phonemes, for example, may combine to form syllables and syllables to form phonological words (“phonological word” is defined as the domain of some phonological process such as accentuation, assimilation, or dissimilation), but the morpheme (or morph) will not necessarily consist of an integral number of syllables, still less of a single syllable. Nor will the word as a grammatical unit necessarily coincide with the phonological word. Similarly, the units of lexical analysis, sometimes referred to as lexemes (in one sense of this term), are not necessarily identifiable as single grammatical units, whether as morphemes, words, or phrases. No priority, then, is ascribed to any one of the three modes.

The originality of tagmemic analysis and the application of the term tagmeme is most clearly manifest in the domain of grammar. By a tagmeme is meant an element of a construction, the element in question being regarded as a composite unit, described in such terms as “slot-filler” or “function-class.” For example, one of the tagmemes required for the analysis of English at the syntactic level might be noun-as-subject, in which “noun” refers to a class of substitutable, or paradigmatically related, morphemes or words capable of fulfilling a certain grammatical function, and “subject” refers to the function that may be fulfilled by one or more classes of elements. In the tagmeme noun-as-subject—which, using the customary tagmemic symbolism, may be represented as Subject:noun—the subject slot is filled by a noun. When a particular tagmeme is identified in the analysis of an actual utterance, it is said to be manifested by the particular member of the grammatical class that occurs in the appropriate slot in the utterance. For example, in the utterance “John is asleep,” the subject tagmeme is manifested by the noun “John.” Tagmemicists insist that tagmemes, despite their bipartite structure, are single units. In grammatical analysis, the distribution of tagmemes, not simply of classes, is stated throughout the sentences of the language. Subject:noun is a different tagmeme from Object:noun, as it is also a different tagmeme from Subject:pronoun.

 Hierarchy of levels

Within the grammar of a language there is a hierarchy of levels, units of one level being composed of sequences of units of the level below. In many languages, five such levels are recognized, defined in terms of the following units: morpheme, word, phrase, clause, and sentence. (The term level is being used in a different sense from that in which it was used earlier to refer to phonology and grammar.) The difference between morphology and syntax is simply a difference between two of these five levels, no greater than the difference, for example, between the phrase level and the clause level. Normally, tagmemes at one level are manifested by units belonging to the level below: clause tagmemes by phrases, phrase tagmemes by words, and so on. Intermediate levels may, however, be skipped. For example, the subject tagmeme in a clause may be manifested by a single word in English (e.g., “John,” “water”) and not necessarily by a phrase (“the young man”). It is also possible for there to be loop-backs in the grammatical hierarchy of a language. This means that a unit of higher level may be embedded within the structure of a unit of lower level; for example, a clause may fill a slot within a phrase (e.g., “who arrived late,” in “the man who arrived late”).

In regard to the notation of tagmemics, a construction is symbolized as a string of tagmemes (which commonly, though not necessarily, will be sequentially ordered according to the order in which elements manifesting the tagmemes occur in utterances). Each tagmeme is marked as obligatory or optional by having preposed to it a plus sign (+) or a plus-or-minus sign (±), respectively. For example, a formula representing the structure of a clause composed of an obligatory subject tagmeme, an obligatory predicate tagmeme, and an optional object tagmeme might be Cl = + S:n + P:v ± O:n (in which Cl stands for a clause of a certain type and n and v stand for the classes of nouns and verbs, respectively). This formula does not represent in any way the fact (if it is a fact) that the predicate tagmeme and object tagmeme together form a unit that is one of the two immediate constituents of the clause. It is one of the characteristic features of tagmemic grammar that it gives much less emphasis to the notion of constituent structure than other American approaches to grammatical analysis.

Stratificational grammar

This system of analysis (whose principal advocate is Sydney M. Lamb, a U.S. linguist) is called stratificational because it is based upon the notion that every language comprises a restricted number of structural layers or strata, hierarchically related in such a way that units or combinations of units on one stratum realize units or combinations of units of the next higher stratum. The number of strata may vary from language to language. Four strata have been recognized for English, and it is probable that all languages may have at least these four: the sememic, the lexemic, the morphemic, and the phonemic strata. The sememic stratal system constitutes the semology of the language; the lexemic and morphemic stratal systems constitute the grammar (in the narrower sense of this term); and the phonemic system constitutes the phonology. In some later stratificational work, the term grammar covers the three higher stratal systems—the sememic, the lexemic, and the morphemic—and is opposed to “phonology.” The deep structure of sentences is described on the sememic stratum and the surface structure on the morphemic. In the present account, “grammar” is used in the narrower sense and will be opposed to “semology” as well as “phonology.”

The originality of stratificational grammar does not reside in the recognition of these three major components of a linguistic description. The stratificational approach to linguistic description is distinguished from others in that it relates grammar to semology and phonology by means of the same notion of realization that it employs to relate the lexemic and the morphemic stratal systems within the grammatical component. Another distinguishing feature of stratificational grammar, in its later development at least, is its description of linguistic structure in terms of a network of relationships, rather than by means of a system of rules; linguistic units are said to be nothing more than points, or positions, in the relational network.