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X is the center of XY (or of Y), and Y is the adjunct of XY (or of X) in sentences S1, if for every S1 we can obtain a sentence S2 by replacing XY by X, but not in general by replacing XY by Y, and if X is the smallest part of XY for which this holds. X, Y range over the set of word-categories defined for each language; for certain purposes they can be taken to range over the individual words or morphemes (word-parts) of the language. If for every sentence composed of the class or constituent (§ 2.7) sequence ABC there exists a sentence AC, the centers are A and C; but this definition would not specify to which center B is the adjunct. If, in addition, for every sentence ABD there exists a sentence AD, we can add to the definition that Y is adjunct of X only if in all sentences of the form S2 (here = AC ⋁ AD) every X is replaceable by XY yielding a sentence (an S1). The analysis is of interest, of course, only if S2 (and S1) are convenient types of S for a characterization of language structure, not if they leave inconvenient residues of S types. If X is the center of some sentence section, and X also appears elsewhere in S1, a unique decision as to which occurrence of X is the center requires the addition either of simplicity conditions (over the structure of the adjunct or the types of S in which X is center) or else of co-occurrence similarities (X1 and not X2 is the center if, in the set of word-triples for which X1X2Y occurs, the dependence of X1 values on Y values is great in comparison with the dependence of X2). With a definition thus strengthened, the choice of centers is unique, including the center ∑ of a whole sentence, except in unimportant respects (e. g. in X and X, either X could be taken as center).
However, the assignment of word sequences to substrings is not unique; so that for some sentences, the fact that a sentence is a case of one structure does not exclude its being recognized as also a case of some other structure.
As before, the structural assignment need not be unique: a given word in a given position may fit into two or more structural assignments. This is not a failure of the computation, but a specific and known homomorphic mapping (homonymous ambiguity) of the set of structures onto the set of sentences.
The major word categories are: A adjective (recursive,...), N noun (operation,...), V verb (recognize,...), T article (the,...), W tense or auxiliary (-ed, will,...), P preposition (of,...), D adverb (recursively,...),C conjunction (and, because), V+ verb with its full object (took the book, elected the man president), V− verb with one ̄N or ̋N missing from its object (took, elected president). Vi + i indicates that the object is of type i which is called for by a V of subset i. (The matching subscripts may be omitted, since they are understood); see note 17. S sentence, ∑ sentence-center; for the major S type considered here, ∑ is NWVi + i.
G(N) itself does not in turn produce a new N, and hence is not recursive. But in some cases it is formed out of some other recursive operation: If G′(P) is the left concatenation of P onto P, forming e. g. over near from near, and out over near from over near, etc., we have: G′(0, Pi) = P = P0 and G′(n,Pi) = Pi+1. Then G(N) consists in the left concatenation of Pi (i. e. of the resultant of G′(P)) to N.
Although a greater number of repetitions, or a wider variety of words in the adjoined substrings, gives an increasingly bizarre effect (in different degrees for different operations).
There are various additional operations of this type. E. g. Fa- operates on N to yield compound nouns (A-N: wild-flowers); thus Fn and Fa- both produce Nn and can operate on each other’s resultants. Fn can also operate on A (including Wing and Wed) to yield compound adjectives (N-A: stone-cold). Fa can in some cases operate on Np (i. e. Na 0 = Np i) as in a veritable bull in a china shop.
Fd can operate on A even when it is not part of Na: This is very nice. But Fa operates only on Na; A appearing elsewhere are not repeatable: we don’t have This is nice old. V (not all) with-ing,-ed can also be adjoined by Fa; or additional operators have to be set up for them: burning interest, broken tubes. We do not say that Fd operates on Na, since it does not operate on Na 0 (e. g. on N-N or on N). We cannot say that Fa adjoins Ad to Na, because only the exterior A can be preceded by D; i. e. Fd operates after Fa: there is no DADAN (without commas). Fd also operates on PN: completely at ease.
We do not write Nd, since this would indicate a recursive operation on N, and would include the non-existent Fd on Na 0. If either the operator Fx or the operand Y are limited, we write Fx.Y for their permitted resultants, not Yx i. A number of detailed restrictions are omitted in this survey. Also omitted are distinctions among some operators (and hence some word-classes) which are grouped together into Fq and into Fe.
Ar·Fp (and Ar with several other Fr, chiefly Fk and Fe, the various F not repeated) is itself a right operator (with difficulty repeatable) on N; we may write it F-a: children lost in thought.
Ft-also (infrequently) adjoins a hyphenated to V— to the right of A; the resultant may be written Ar, with Ar 0 = A: a hard-to-distinguish thin line. (The to V— is not hyphenated when Ar is not in Na: This is hard to distinguish.) There are other infrequently-met operators which hyphenate strings to the right of A in Na, or simply adjoin the strings to A.
There are other, less-frequently occurring, right operators both on N and on V-containing strings. A right substring which is adjoined almost only to ∑ is , which NWV-,: as in I found her there, which I had long hoped to do.
I. e. (a) N, W, WV, etc.; (b) N-, A, D, PN, Wing+, Wen+, wh-strings, NVing +, C4 NWV +, etc.; (c) Na, Ad, Nr, Ar, YCY, etc. In addition, Y can be Ft.Ad and Ft.Fn (the old and the new plans and the dress and the shoe sales); and there are some special and infrequent cases, such as the value of Y being two non-contiguous constituents: e. g. the subject and the object, as in He speaks English and I French. Among the types of strings excluded from the values of Y are (aside from certain special cases) the adjoinings due to two or more operations (which may be the same); e. g. there is no AACAA: nice large and new beautiful (without comma).
Subsidiary sentence types are chiefly: sentences in which certain N-replacer substrings, not adjoined to N, occupy the position of N in the major type; questions; imperatives; object-subject-verb arrangements.
One member of W is zero. If we do not admit zero members, we would have to say that W may or may not occur here.
For example, the subset Ve (containing the single verb have, which is also a member of other subsets) has as object W ien +i (i. e. a verb of any subject i plus the suffix en plus the object of type i); the subset Vg (is, like, etc.) has as object W iing + i; the subset Vn (sell, find) has N; the subset Vnt (find, know) has N toVi + i; etc.
In Vi−i, the — equals: +i minus one ̋N; or +iP (i. e. +iP̄N minus the last ̄N). ̄N is a match between (a) the set of strings produced by the N′ generator and (b) the sequence of marks to the left of each N in a sentence; the first approximation to ̄N t is the longest string (out of b) which ends on the right with this N and which is a member of the set N′. A second approximation is obtained if part of the ̄N can be reassigned to some other element in the well-formedness of the sentence: e. g. the ANN = ̄N may be reassigned into TA = ̄N plus NN = ̄N, or into TAN = ̄N plus N = ̄N (both yielding two ̄N in the sentence); ACAN = ̄N may be assigned into A (as an object) plus C plus AN = ̄N and into D (as object or right identity) plus C plus DAN = ̄N (if an appropriate V precedes).
Repetition with C of any circled element X or any succession of these XY, i. e. the adjoining of CX to X and of CXY to XY, is not shown here, but is to be carried out in accordance with 2.7.
In certain positions, e. g. the second ̋ of an object, few or none of these strings can besubstituted for ̋N. Note that while Fr produce adjunct strings adjoined to an N′ (and together with that N’ constitute an ̋N-string), the N-replacers are strings (mostly similar to some Fr) which occupy the position of an N′ in an including string.
The local-tree network can be completed by considering the dictionary also to be a tree, which in this case follows not the sequence of a text, but the sequence in the matched word and classification in the dictionary. (The entry — the word — reaches immediately to the output; but the analogy to the tree will become useful when we consider the variable output here as in the later trees.) Symbols from the computer program of TDAP16-20 are: T1 = a, an; B = adjectivized pronouns (e. g. their); R = pronouns; T2 = the; Q == quantifiers (e. g. few); M = words not in the dictionary (mostly nouns); L= numbers; G = V + ing; S = V + en; N7 = measure nouns (e. g. minutes).
See 5.2, 3.
The two relations of sentence-center to sentence (note 1 and 6.1) are not a surprising correlation, but the result of simplicity considerations in the construction of the analysis. The categories in respect to which the adjoinings were recursive (in 1 above) were determined on this basis: roughly, ̄Ni is that set of word sequences that can replace N0 (i. e. N) in a sentence.
Ad indicates D composed of A plus the adverbializing suffix-ly; An indicates N composed of A plus nominalization (in this case, the dropping of-ful). Various restrictions on the correspondences of substring and sentence are not mentioned here, but will be discussed in a later paper.
Under given conditions, these substrings correspond to other sentence transforms. For example, if Fp contains Wing of N2, the corresponding sentence is often N2 WV + (where + is zero): barking of dogs — dogs bark.
The substring adjoined, usually between commas, by Fn, is more exactly not ̋N but any string which can be the object of is in a sentence; compare the operator Fk.
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© 1970 Springer Science+Business Media Dordrecht
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Harris, Z.S. (1970). Computable Syntactic Analysis: The 1959 Computer Sentence-Analyzer. In: Papers in Structural and Transformational Linguistics. Formal Linguistics Series. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-6059-1_16
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