the use of matrix technique in an analysis of atta ...reid/combined files/a06. 1964....

The Use of Matrix Technique in an Analysis of Atta Personal Pronouns

Ruth Lusted; Claudia Whittle; Lawrence A. Reid

Oceanic Linguistics, Vol. 3, No. 1, Papers in Philippine Linguistics. (Summer, 1964), pp.138-160.

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http://www.jstor.orgSat Feb 16 23:53:41 2008

THE USE O F MATRIX TECHNIQUE IN AN ANALYSIS OF A T T A ~PERSONAL PRONOUNS

Ruth Lusted, Claudia Whittle, and Lawrence A . Reid

0. Introduction

1. Permutat ion and Conflation

1. 1 Listing of Pronouns

1. 2 Stages in Pronoun Matr ix Permutation

1. 3 Conflation

2. Semantic Microanalysis

2.1 Formatives for Person and Number

2. 2. Format ives of Aspect and Grammatical Relationships

3. S u m m a r y

0. Introduction. All Philippine languages have multiple pronoun se t s , differing in distribution within the clause, and differing in internal complexity. Traditionally, pronoun se t s have been listed and their distribution stated, but few attempts have been made to describe their internal s t ructuring. Smearing of morpheme boundaries has made conventional morpheme analysis of the pronouns a difficult and often unproductive exercise . It will be demonstrated in this paper , however, that by using the techniques of mat r ix permutation and conflation, the ranking of pronouns and a display of their internal s t ruc ture i s entirely possible. The purpose of this paper i s , f i r s t , to demonstrate how this was accomplished for the Atta pronouns, and second, to show how on the basis of these mat r ices meanings can be attributed to each of the pronoun formatives.

1. Permutation and Conflation. F i r s t a conventional listing of Atta pronouns i s given. Then, s tages i n the mat r ix permutations

of the pronouns a r e described, and finally the resultant mat r ix i s conflated to reveal ranking of the pronouns and the patterning of their formatives.

1.1 List. g of Pronouns. Four se t s of personal pronouns t?occur in Atta. Set I pronouns occur a s topic of a c lause, Set I1 a s source, Set 111 a s oblique, and Set IV a s emphasis ( s e e Matr ix 1). In the mat r ices person 1 represen ts speaker when s ingular , speaker and companion(s) when plural. P e r s o n 1 ,2 represen ts speaker and addressee in the singular; speaker , addressee , and companion(s) of e i ther o r both i n the plural. P e r s o n 2 represen ts addressee in the singular, addressees in the plural. Persona 3 represents referent when s ingular , referents when plural. Matr ix 1 consis ts of a conventional listing of the pronouns.

8Matrix 1.

Singular P lura l Set I

1 aq kami 1, 2 i t ta i t tam 2 kayu 3 i r a

Set I1 1 mi 1, 2 t am 2 naw 3 da

Set 111 nikaan nikarni nitta nittam nikaw nikayu kuna n i ra

Set IV 1 sikaan sikami 1, 2 si t ta s i t tam 2 sikaw sikayu 3 aggina aggira

1. 2 Stages i n Pronoun Matr ix Permutation. F r o m the above listing of the pronouns Matr ix 2a was s e t up. The four s e t s f o r m the columns; person f o r m s the rows with singular persons grouped preceding plural persons. The formatives g i n Set 111 and & in Set I V become apparent i n Matr ix 2a and these formatives a r e shown in the abstracted formative m a t r i x 2b. However, the

-ni block of 111i s broken by the occurrence of & in s 3 and the & block of IV i s broken by % i n s 3 and p3.

Matr ix 2a.

$

1

I

aq

I1

ku

ILI

nikaan

IV

sikaan

1, 2 i t ta t a nitta s i t ta

2 ka mu nikaw sikaw

3 # na kuna aggina

P 1 karni mi nikami sikarni

1, 2 i t t am t a m ni t tam s i t t am

2 kayu naw nikayu sikayu

3 i r a da n i ra aggira

In o rder to bring the 2,g,3,and & formatives into unbroken blocks, Matr ix 2a was then rear ranged so that the singular and plural categories appear in columns instead of rows (Mat r ix 3a). This brings together the block in Set 111, al l persons except s3, which itself fo rms a block of &; the &block in Set IV , persons 1, 1, 2, and 2; and the ag block in Set IV, person 3 ( s e e abstracted formative mat r ix 3b).

Matr ix 3a.

1 aq kami ku m i nikaan nikami sikaan sikami 1 ,2 itta i t t am ta t a m nitta nittam si t ta s i t t am 2 ka kayu mu naw nikaw nikayu sikaw sikayu 3 # i r a na da kuna n i ra aggina aggira

Matr ix 3b.

Having observed the pat terns of pronoun-initial iormatives in the columns of Matr ix 3a, pat terns were then seen emerging in pronoun-ending formatives in the rows, for example the formative s

-ta alternating with tam i n person 1, 2, and the & and formatives i n person 3. Since these cannot be a s readily seen in rows a s in columns, i t i s advantageous to permute Matr ix 3a so that the persons a r e shown i n columns and the s e t s in blocks of singular and plural a r e shown In rows (Matr ix 4a). Notice also the regrouping of the singulars and plurals together, destroying for the moment the previous blocks of G, 2,s,and &, but bringing together new like-formatives. These formatives a r e seen in Matr ix 4b.

Matrix 4a.

I aq itta ka # I1 ku ta mu na III nikaan nitta riikaw kuna IV sikaan s i t ta sikaw aggina

I kami i t tam kayu i r a I1 m i t am naw da 111 nikami ni t tam nikayu n i ra IV sikami s i t t am sikayu aggira

Matr ix 4b.

*The 5alternating with & occurs a s a resul t of a morphophonemic change in which d becomes r following vowels.

A formative was then noted appearing inter ior in the composites of some cel ls of persons 1 and 2 vectors. To group these in a block, and a l so to place into adjacent columns the

formative blocks already identified, Matr ix 4a was permuted to group singular and plural with each person, and to cause person 1 ,2 singular and plural to appear between person 2 and person 3. This brings the &block to the left of the mat r ix , occurr ing in persons 1 and 2 (Matr ix 5a).

At this stage two more formatives may be identified and placed with & in abstracted formative mat r ix 5b. These are^ (occurr ing a s the final consonant of the f i r s t syllable of each of the bisyllabic pronouns of 1,2 person) , and g (occurr ing a s the f i r s t consonant of the inter ior syllables of person 3 of Set IV) .

Matr ix 5a.

I aq kami ka kayu itta i t tam if i r a I1 ku m i mu naw ta t am na da 111 nikaan nikami nikaw nikayu nitta nittam kuna nira I V sikaan s ikami sikaw sikayu s i t ta s i t tam aggina aggira

Matr ix 5b.

Examination of any of the preceding mat r ices reveals that Sets I11 and IV a r e m o r e complex than Set I , and Set I in turn i s more complex than Set 11. A ranking of complexity becomes evident, suggesting the poasibLlity of implications in the semantic analysis. In o rder to show clear ly the ranking of complexity the rows I and I1 were interchanged (Mat r ix 6).

Matrix 6.

1

11 ku m i mu naw ta t am na da

I aq kami ka kayu i t ta i t tam # i r a

111 nikaan nikami nikaw nikayu nitta nittam kuna nira

IV sikaan sikami sikaw sikayu s i t ta s i t t am aggina aggira

It may be noted that columns lp, 1, 2s, and 3p in Matr ix 6 a r e more regular than the other columns in that the final syllable remains the same throughout the four sets . In Matr ix 7 the regular

columns a r e grouped on the left half of the matrix. In addition the

rows a r e inverted to display a different perspective with greatest complexity appearing in the top row, l eas t complexity in the bottom row.

Matr ix 7.

IV sikami s i t ta s i t t am aggira sikaan sikaw sikayu aggina 111 nikami nitta nittam nira nikaan nikaw nikayu kuna I kami itta i t tam i r a aq ka kayu # I1 m i ta tam da ku mu naw na

By Matr ix 7 a grouping of regular columns was achieved. It has lost however the regular i ty of rows with & a s seen in Matr ix 5a and 5b. Because of the des i re to p reserve both the column regular i ty of Matr ix 7 and the row regular i ty of Matr ix 5, Matr ix 8 was se t up, in which the plural was placed before the singular with each person.

Matrix 8.

1

P S P s P S P s

I V s ikami sikaan sikayu sikaw si t tam si t ta aggira aggina

111 nikami nikaan nikayu nikaw nittam nitta n i r a kuna

I kami aq kayu ka i t tam i t ta i r a -ti

I1 m i ku naw mu t a m ta da na

1.3. Conflation. Having found by permutation a l l the apparent formative blocks in the mat r ices , including single-cell blocks containing ideal par t ic les , l1 a conflation of the formative blocks of Matrix 8 was made in Matr ix 9 to portray the patterning and field s t ruc ture of Atta personal pronouns.

2. Semantic Microanalysis. Matr ix 9 contains two complex- i t i es relevant to semantic description: (1) The columns a r e composed of two types of lexical categories--person and number. (2) The rows contain not lexical categories , but s t ruc tura l categories .

2.1 Format ives fo r P e r s o n and Number. The s implest of the pronoun se t s i s Set 11, which contains the semantic components of person and number. The pronouns of Set I1 ( represen ted by one hyphen each in the bottom row of Matr ix 9) a r e enclosed by only one block each, with the exception of person 1, Zp, which i s a lso enclosed by an inter ior =block. Several of these blocks, i. e. , lp (mi),1, 2p (Eand m), 1, 2s (E),and 3p (&), extend vertically without a break throughout the four s e t s of pronouns. The formatives in these vert ical blocks contain the semantic components of person and number i n the m o r e complex pronoun s e t s a s well. These a r e blocks of vector formatives, which a r e equivalent to conventional morphemes. l3 The remaining vert icals , i. e. , f r o m columns Is , 2p, 2s, and 3s of Matr ix 9, a r e broken i n one or two places, reflecting alloformatives, o r a l lomorphs, for person and number.

In describing the distribution of the person and number formatives, i t i s convenient to abs t rac t pa i r s of submatr ices fo r each pronoun se t , separat ing the person and number formatives. This segmentation i s perhaps of f iner detail than that of previous conventional treatment.

Matr ices 10 and 11 a r e abstracted submatr ices fo r Sets I11 and IV, containing the formatives fo r person and number. Sub-mat r ices fo r these two pronoun s e t s a r e used to symbolize the emic norm of the various mat r ices of the four s e t s of pronouns for the following reasons: (1) Identical categories a r e found i n each of the matr ices . ( 2 ) There i s a l a rge percentage of identical formatives throughout the matr ices . ( 3 ) P e r s o n and number formatives of Sets I11 and IV a r e homophonous throughout. (4) The alloformative variants of the person and number formatives i n the four se t s of pronouns a r e non-contrastive etic var iants , conditioned in one of--or a combination of--the following ways: phonologically conditioned, o r conditioned morphologically by the co-occurrence of morphemes of aspect o r grammatical relationship, o r indirectly conditioned by the distribution of each s e t within a different tagmemic slot.

Matr ices of alloformatives for person and number i n Sets I and I1 a r e not presented since they show only slight etic ver iat ion

f r o m the n o r m shown in M a t r i c e s 10 and 11. However , i n the textual desc r ip t ion of the m a t r i c e s fo r Se t s 111 and IV, va r i a t ions of the m a t r i c e s f o r Se t s I and I1 wi l l be stated.

2. 1. 1. Determining Segmentation. The p rocedure f o r de t e rmin ing the segmentat ion of the fo rma t ives of t hese subma t r i c e s by examinat ion of the ve r t i ca l blocks of Mat r ix 9 i s desc r ibed In deta i l i n the next s e v e r a l pa rag raphs .

M a t r i x 10. E m i c F o r m a t i v e s fo r Pe r son .

P e r s o n : 1 2 1, 2 3

Number:

P - i -u ta - -a

Mat r ix 11. E m i c F o r m a t i v e s f o r Number.

P e r s o n : 1 2 1, 2 3

Number:

Submat r i ces 10 and 11 have a n ident ica l a r r a n g e m e n t of ca t egor i e s ; the columns conta in ca t egor i e s of p e r s o n (1 speake r ; 2 a d d r e s s e e ; 1, 2 speake r and a d d r e s s e e ; 3 r e f e r e n t ) , which i n t e r s e c t with ca t egor i e s of number ( p p lu ra l , s s ingu la r ) i n the rows. E m i c fo rma t ives fo r pe r son f r o m Se t s I11 and IV appea r in the ce l l s of Mat r ix 10, with hyphens indicating the posit ion of the number fo rma t ives . Ma t r ix 11 conta ins e m i c fo rma t ives fo r number f r o m S e t s 111 and IV in the c e l l s , with hyphens indicating the posi t ion of the p e r s o n fo rma t ives .

In Mat r ix 9 , columns of p e r s o n 1, 2 a r e cove red with a 2 block in both s ingular and p lu ra l ; t he re fo re 5i s p laced in the 1, 2

vector of Matrix 10 a s person 1, 2 formative. P lura l 1, 2 i s contrasted with singular by the in te r io r 2 block; therefore 2 i s placed in the cel l a t the intersect ion of plural with 1 , 2 i n Matr ix 11 a s a plural formative. Singular with person 1, 2 can be analyzed a s consisting of e i ther a ze ro alloformative, o r without 2 The second analysis has been chosen a s preferable; i t seems awkward to at t r ibute the singular component intersecting with person 1, 2 to ze ro when, by cont ras t with 1, 2 plural , the singular component actually seems to be signaled by absence of the plural formative. Pike has adopted the use of an acute accent m a r k af ter the formative to indicate i t s obligatory absence. l4 Using this notation, formative m- i s placed in Matr ix 11 a s the singular formative which in te rsec t s with person 1, 2. The submatr ices for Sets I and I1 ( not shown) contain no variants f r o m the formatives seen in Matr ices 10 and 11 in these categories .

Second person singular of Set I i s enclosed in a ze ro block in Matr ix 9 and can be described a s manifested by a ze ro alloformative for person 2 and singular, o r by a different ze ro for each component. A third alternative may be preferable. The only over t formative whict occurs in Set I with 2s i s &, which has been included with the hori- zontally extensive &block of Matr ix 9. This & can be analyzed a s portmanteau when occurr ing alone, containing semantic components of person 2 and singular a s well a s the component for Set I. However, since the &formative i s f r o m a different formative layer , and in o rder to facilitate this description, the single ze ro alloformative will be used in this paper to represen t both person and number components of 2s in this set.

The person 1 formative of Matr ix 9 i s abstracted next. Since person formatives in the other cel ls a r e vowels and mhas already been determined a s a plural formative intersecting with person 1, 2, although i ts position var ies in relat ion to the person formative (i. e. , i t occurs before person 1, but af ter 1 ,2 person) , the m - formative for plural i s placed i n Matr ix 11 where plural in te r sec t s with person 1. Formative a s person 1 ( f rom the inner layer vert ical block of lp--not to be confused with the horizontal outer l a y e r 2 block) i s placed in the cel l a t the intersect ion of person 1 with plural in Matr ix 10. There a r e no variants of formatives for lp among the four sets of pronouns; mi in vert ical block lp of Matr ix 0 i s a vector-patterned formative, o r morpheme.

Finally, f r o m column 1s of Matr ix 9 the 1s formative -ani s abstracted. F r o m the r ight hand column of Matr ix 9 , 3s , formative

-n has already been identified a s a singular formative intersecting

with person 3 . Consistent with the analysis of the other formatives, the -2 of 1s i s analyzed a s indicating singular here a s well. The vowel i s chosen a s the person formative, although the order of the formatives varies here also (compare 1,2p with lp above), i. e . , in 3s the o rder i s number formative followed by person formative, but here in 1s the o rder i s person formative followed by singular formative. Formative a- a s person 1 i s placed in Matr ix 10 at the intersection of person 1 with singular. Formative -n a s singular i s placed in Matr ix 11 a t the intersection of singular with person 1.

Sets I and I1 have alloformative variants of Is , seen in the broken vert ical block of column 1s in Matr ix 9. Set I variant i s -3,8 with the vowel formative retained, but -2a s an alloformative of -n for singular. Set I1 variant i s &, analyzed a s &- fo r singular and -u for person 1. -

2. 1. 2. Listing of Formatives. The alloformatives f rom al l four se t s of pronouns and their meanings, a s described in the preceding paragraphs, a r e s tated a s follows, using the notation adopted by Pike. 16 ( U , to be read ' o r ' , represents the union of two categories;n, to be read 'and ' , represents the intersect ion o i two categories. ) Alloformatives have been listed f rom Matrix 9 In o rder i r o m left to right by columns and f r o m top to bottom by rows.

plural U singular. person 1. person 1 U person 3. singular. singular. singular. person 1 U person 2. plural. plural. person 2. (pe rson 2 U person 3) tI singular.

--t a - person 1, 2.

-d-f = plural.

2. 1. 3. Listing of Categories. In the above list , ambiguities a r e apparent; however, when categories of person and number intersect , these ambiguities a r e resolved. The categories a r e listed and described below f r o m Matr ix 9 i n the same order a s stated above. (A hyphen i s used with the interesecting forrnatives to indicate o rder of occurrence. )

=person 1 (in=) U ( an[zu 5 1 ) u (un-k-). person 2 = (un[zU m-1) U (Wn u i ] ) u (# n k ) .

person 1 ,2 = ( tan[=U &I).

person 3 = ( a n[&-=U %]) U #.

plural = ( % n [ s U &]) u ( y n s ) U ( E ~ - w )U

( d ~ ~ n s ) .

singular = ( p n [ ~ U ~ ] ) U ( q n ~ ) U ( [ & U m ] n ~ )

u ([iu g ] n E ) U (En&) U ( & n k ) .

2.1.4. Matr ix of Kernel Person and Number Formatives. As has been mentioned, the above s tatement includes the alloformatives for person and number for a l l four s e t s of pronouns. The emic formatives (morphemes) for person and number a r e displayed in Matr ix 12, which represen ts the emic kernel17 of the pronoun s t ruc ture and will be symbolized by Mk. At the level of this mat r ix , the ambiguities have disappeared. Each cel l i s filled by a different formative, a single-cell formative; Matr ix 12 i s a n ideal matrix. l8

Mat r ix 12. Mk --Emic Person and Number Formatives.

Person: 1 2 1, 2 3

Mk = Number :

P m i YU t a m da

The occurrence of the alloformatives for person and number in each of the pronoun s e t s has been described above, so that Set I1 pronouns can now be defined i n the simple emic formula--Mk= Set 11.

2. 2. Formatives of Aspect and Grammatical Relationships. The three outer l ayers of horizontal blocks in Matr ix 9 have not

been defined. The inter ior one of these i s composed of blocks of

-ka, J, and g; the middle layer i s the block o f i which occurs exter ior to a n d t , but inter ior to g; and the exter ior layer contains blocks g,&, 2, and 3. These outer blocks extend horizontally within the the rows of Sets IV, ID, and I, but not Set 11, which suggests a s t ruc tura l contrast between the f i r s t three se t s and Set 11. Set I1 has been defined a s consisting simply of kernel pronominal formatives which a r e present in al l four sets. Complex Sets IV, 111, and I a r e derived sets.

2. 2. 1. T h e 2 Block. Set LI pronouns substitute fo r substantive phrases indicating source. Pronouns of Sets IV, 111, and I substitute within a clause for substantive phrases indicating relationships other than that of source. In Matr ix 9 , the middle layer f o r m a t i v e i block extends over a large a r e a of these three sets. In Set I, i o r m a t i v e l , which occurs word initially (except before k, and -aq of i s , which will be explained l a t e r ) m a r k s this se t a s substitutable for a topic phrase i n a clause. Set IV substitutes for a nonemphatic topic phrase in post-predicate position--but changing it to emphatic topic, o r for an emphatic topic phrase in pre-predicate position. Pronouns of Set I11 occur only in oblique relationship within a clause, indicating that the semantic component o f i is modified by the occurrence o i the oblique relationship component.

The anaiysis of i a s carrying the topic relationship component i s interestingly by the identical shape of a f ree v a r i a n t i , in fast speech, of the phrase marking part ic le E,which m a r k s the topic phrase within a clause.

T h e i block does not extend over person 1 and person 2 of Set I o r over 3s of Sets 111 and I. Third singular of Set I has no overt f i l ler ; f o r m a t i v e i i s assumed to occur here a s a ze ro alloformative. Third singular of Set 111 i s completely i r regu la r in i ts outer l ayer , which consis ts solely of &. This &block i s the only i r regular i ty in the row of formative n; therefore & i s analyzed a s an alloformative of 5 and u a s an alloformative o f .

F i r s t person singular of Set I i s the only pronoun in the four se t s which has only a bound ciitic (suffix) fo rm, i. e. , -aq. Since the semantic component of f o r m a t i v e i i s present here also, zero alloformative o f i i s assumed to occur here; and for the same reason, the ze ro alloformative of i i s a lso assumed to occur word initial -before k i n Set I, columns lp, I s , 2p, and 2s. This analysis i s i l lustrated i n Matr ix 13. An al ternate solution would be to consider

IV

the &portmanteau, carrying the topic phrase component a s well a s i t s par t icular component of aspect which i s discussed below.

In formulas f o r the derivation of the different pronoun se t s , the formative semantic component will be symbolized by

-t , reflecting i t s topic marking function.

Matr ix 13. Abstraction o f i Block Showing Alloformatives.

lp 1s 2p 2s 1 . 2 ~ 1, Ls 3p 3s

2. 2. 2. Blocks of &, t , and g. Perhaps the mos t difficult to define of the horizontal outer blocks of formatives a r e the blocks of &,t,and g. These three blocks divide the columns, & extends over person 1 and person 2 of Sets I, 111, and I V , except 1s oi Set 1 where it i s assumed that since the semantic component i s p resen t , a ze ro alloformative of & o c c u r s ; t extends over person 1, 2 in these three se t s , and g extends over person 3 in Set IV only. The only internal clue a s to the meaning of these formatives i s their contrastive distribution, which suggests contrast of aspect.

There a r e other clues a s to meaning f r o m the affixation in the language; ka- i s a productive morpheme which occurs prefixed to s tems ei ther alone o r i n combination with other affixes. The meaning of ka- var ies according to types of s tems with which ~t occurs; fo r example, with descriptive s tems , i. e. , adject ives, i t f o r m s nouns: baddl means ' s m a l l ' , kabaddl means childhood';

-a w i n means 'none', kCwln means 'absence'. 'Specific', 'def ini te ' , and 'superlative' a r e some of the glosses that have been used for

-ka-. With reference to the pronouns, the f i r s t two of these glosses may be pertinent to the &block a s a gloss for i t s aspect meaning in contrast to the aspect meaning of the f o r m a t i v e s t and g described below.

The two remaining formative blocks of this in te r io r horizontal layer a r e blocks o f t and g. These a r e analyzed a s alloformatives of

--

one fo rma t ive r e p r e s e n t e d by morphophonemic _G s n the b a s i s of the following morpho:ogical data:

1. In pref ixes ending i n 9, such a s mag- and =,the g com-ple te ly a s s i m i l a t e s to the in i t ia l consonant of the s t e m , fo rming a geminate consonant c lus t e r . Single g i s r e t a ined only with vowel -in i t ia l s t e m s . F o r example , m e a n s ' t ha t which i s to be f anned ' , plus becomes appeppek ' the f a n 1 , o r p lus m x become s m a g a t 3 ' t o roof1. Th i s morphophonemic change sugges t s that the pronominal f o r m a t i v e t m a y be an a s s i m i l a t e d g .

2. T h e r e i s a nonproductive affix g l -wh ich o c c u r s with s o m e s t e m s e i the r alone o r in combinat ion with o the r affixes. 'ru'onspeci-f i c ' and ' g e n e r a l ' a r e used a s g l o s s e s f o r &with c e r t a i n s t e m s ; f o r example , n u i n g m e a n s ' c a r a b a o ' , m e a n s ' domes t i c fou r - legged an ima l s ' . With s o m e s t e m s =,an a l lomorph of&, o c c u r s f o 1 l o w i n g ~ - , which m e a n s ' a n in s t rumen t ' . The c o n t r a s t of =with

-ka- i s s e e n in the following examples : a m m u m e a n s ' t o know' , g ig i ammusn m e a n s ' s tudying i n s c h o o 1 ' ~ a m m u ~ n ' c o m -m e a n s p rehens ion ' ; ubobuk m e a n s ' w o r d ' , aggubobuk (wplus x)m e a n s ' s p e e c h ' , kobobuk (ka - p lus ubobuk) m e a n s ' r e a s o n f o r speaking ' .

On the bas i s of the da ta , the t f o r m a t i v e , which o c c u r s before pronoun fo rma t ive p e r s o n I , 2 beginning with in i t ia l t, i s analyzed a s an a s s imi l a t ed *, a l lomorph of&, containing the s eman t i c component of ' g e n e r a l ' , and the g fo rma t ive of Set I V i n 3p and 3s i s included i n th is analys is . The t and g blocks a r e then brought together into a s ingle G fo rma t ive block. Metathes is -i s a s s u m e d to have o c c u r r e d between the g fo rma t ive and t h e 1 fo rma t ive , which o c c u r s e x t e r i o r to the blocks of ka and 5 except -i n 3p and 3s of Se t IV.

However , t h e r e a r e s o m e inde te rminac ie s connected with this analys is . The ca t egor i e s of 3p and 3s i s Se t s I and LU a r e not inc luded in the _G block. Should these two s e t s be included by postulating a z e r o a l loformat ive of _G? O r i s the p e r s o n 3 ca t egory of S e t s I and 111not included i n th is fo rma t ive block because i t s s e - man t i c components of this c l a s s wi l l be symbol ized by%, ref lec t ing the c l a s s meaning of aspect .

Matrix 14. Abstraction of Blocks of & and G Showing Zero Alloformatives.

2. 2. 3. Derivation of Set I. Of the horizontal blocks of formatives, the occurrence of the in te r io r and middle l ayers , and G a n d i , contrasts Set I pronouns with Set 11. Since Set I1 pronouns have been defined in Matr ix 12 a s Mk, it i s now possible to derive Set I by mat r ix multiplication, applying h e r e the procedure outlined by Pike, l9 i. e., the kernel mat r ix is assigned a symbol-- Mk; the factors & and G a r e symbolized by a (for aspect fac tor ) , a n d i i s syrr.bolized b y t (topic phrase) ; a derived m a t r i x i s the product of multiplication of a kernel matr ix. The product of this multiplication (Formula 1) i s a derived single row vector mat r ix identical with the third row down abstracted f r o m Matr ix 9 (i. e . , Set I pronouns), which will be labeled Mt since this i s the se t which occurs a s topic within a clause.

Formula 1. Mk ' a . t :Mt

2. 2. 4 Blocks of n and s. Yet remaining to be described a r e the exter ior horizontal l ayers extending over Sets I11 and IV, which a r e composed of two mutually exclusive contrastive row vec- tors . The lower one may be represented by formative 1,which includes the alloforrnative k intersecting with 3s; the top row vector may be represented by formative 2, which includes the alloformative intersect ing with 3p and 3s.

The formatives of these blocks, 1 .U k and 2 --. 3, c a r r y the s t ruc tura l signals which cont ras t Sets III and IV respectively and indicate their syntactic relationships. Set III pronouns a r e substitutable for phrases i n oblique relationship within a clause; the oblique relationship i s the grammatical semantic component of 2 --. k . The 2 --. of Set IV pronouns c a r r i e s the semantic component of topic emphasis , and indicates substitutability of

t hese pronouns f o r a topic p h r a s e (Set I pronouns occur h e r e a s nonemphat ic topic) o r f o r a n emphat ic topic p h r a s e , which o c c u r s i n p re -p red ica t e posit ion.

When a name i s subst i tu ted fo r a pronoun in a topic p h r a s e o r an emphat ic topic p h r a s e ( p r e - p r e d i c a t e ) , the name i s p receded by pe r sona l mark ing pa r t i c l e 5 But th is co r re l a t ion of shape of pronoun fo rma t ive f o r emphat ic topic re la t ionship with the shape of the pe r sona l mark ing pa r t i c l e indicating the s a m e re la t ionship i s not pa ra l l e l ed i n the c a s e of oblique p h r a s e s ; when a n a m e subs t i tu t e s f o r a pronoun in a n oblique p h r a s e posit ion, i t i s p r e - ceded by the pe r sona l m a r k i n g pa r t i c l e E.

The pe r sona l mark ing pa r t i c l e g o c c u r s before n a m e s only in a t t r ibur lve re la t ionship indicating s o u r c e ; only pronouns of S e t I1 occur he re .

2 . 2. 5. Derivat ion of Se t s III and IV. Se t 111 pronouns can be de r ived Sy multiplying the m a t r i x of Set I pronouns , Mt, by the constant f ac to r 1 - k (oblique r e l a t ionsh ip ) , which will be symbol ized by 2. The product of this mul t ip l ica t ion ( F o r m u l a 2) i s a de r ived singie row vector m a t r i x ident ica l with the second row down of M a t r i x 3 (i.e. , Se t I l l p ronouns ) , and th is m a t r i x will be labeled Mo, ref lec t ing i t s oblique g r a m m a t i c a l re la t ionship .

F o r m u l a 2. Mt ' o = Mo

S imi la r ly , Set IV pronouns a r e de r ived by mul t ip l ica t ion ( F o r m u l a 3) of Mt by the constant f ac to r 2 * ( empha t i c topic r e l a t ionsh ip ) , which wi l l be symbol ized by 2. The re su l t an t de r ived s ingle row vector m a t r l x i s ident ica l to the f i r s t row of M a t r i x 9 ( i . e . , Set IV p ronouns ) , and i s given the symbol Me, ref lec t ing the emphat ic component of the set .

F o r m u l a 3. Mt e = Me

3 Summary . The in t e rna l s t r u c t u r e of fou r s e t s of At ta pronouns w a s graphical ly d isplayed i n the m a t r i c e s of Sect ion 1. In Sect ion 2 the seman t i c components of t hese pronoun s e t s w e r e d e s c r i b e d and r e l a t e d to the g r a m m a t i c a l cons t ruc t ions i n which they occur

Using m a t r i x mul t ip l ica t ion, the der ivat ion of the m o r e complex S e t s I, 111, and IV f r o m the k e r n e l S e t I1 was reduced

to three s imple formulas, reflecting the relationship of the se t s to each other , both s t ructural ly and semantically.

NOTES

1. Atta is a Negrito dialect of Northern Gagayan Province, Luson, Philippines. Data were gather.ed by Whittle and Lusted in the municipalities of Pamplona, Cagayan Province, and Allacapan, Cagayan Privince, during the y e a r s 1955-63.

2 . See Otto Scheere r , "The Nabaloi Dialect," Ethnological Survey Publications, Manila, 1905, Vol 11, P a r t 11, pp. 113-117; Rufino Alejandro, & Handbook of Tagalog Grammar , Manila, 1947, Chapter 10; Andrew M. Nelson, & G r a m m a r of the Cebuano Dialect, Ago Mimeograph Service, Cebu City, Philippines, 1954, Chapter 4; Morice Vanoverbergh, CICM, Iloko G r a m m a r , Catholic School P r e s s , Philippines, 1955, Chapter 5; Jose Hevia Campomanes, 0. P. , G r a m m a r of the Tagalog Language, c i r c a 19th century, p. 16; Howard McKaughan, The Inflection and Syntax of Maranao Verbs, Manila Bureau of Printing, 1958, p.8.

3. David Thomas, in his "Three Analyses of the Racano Pronoun System, ' I Word, 2: 204-208? 1955, breaks down some of the m o r e complex Ilocano pronouns, and assigns meaning to the separated morphemes. He s tates (p. 205, footnote 6), "I have pre fe r red to analyze these ' f ree pronouns' a s bound pronouns suffixed to a particle of emphasis, r a ther than analyzing the total f o r m a s a f r e e pronoun." McKaughan, 9.s t . , s ta tes , p 8, "Inspection shows that a t l eas t some of these se t s consis t of combinations of bound morphemes with perhaps allomorphs of pronominal basis.. . morphemes could be isolated in Sets I and I1 with an attempt to relate such morphemes to grammatical o r lexical meanings. However, for ease of description and reference, we have listed the members of the paradigms a s units without fur ther analysis. " Phyllis Healy i n her An Agta G r a m m a r , Manila Bureau of Printing, 1960, p. 16, s ta tes ' I . ..i t i s impossible and unprofitable grammatically to t ry to draw morphological boundaries within the fo rms of these pronouns. . . " Agta i s a language closely related to Atta.

4. Kenneth L. Pike, Matr ix Permutat ion &Conflation, presented under the tit le Matr ix Rotation and Matr ix a s a n Emic Unit, to the annual meeting of the Linguistic Society of Amer ica in

New York, Dec. 29, 1962. He defines permutation a s "any inter- change of rows, o r interchange of columns, o r interchange of rows with columns, o r interchange of cel l components f r o m inside to outside the matrix. " (p. 2) Conflation i s "the resu l t of super- imposition--of the blocks of formatives of the various submatr ices ."

(P. 7) .

5. As defined by Pike, 2.c.,"A formative.. . i s the phonological par t ic le filling a cel l of an emic m a t r i x "

6. When Sets I and I1 occur in juxtaposition in the syntax some fusion occurs , forming a pseudo-Set V.

7. Leonard Bloomfield, in Language, 1933, t e r m s plural pronouns like these in Tagalog respectively "exclusive f i r s t person plural" and "inclusive f i r s t person plural. " p.Healy, 2.c.,15, t e r m s person 1 ,2 the inclusive person. F o r a handling of pronominal semantic components in HanunGo, see Harold C. Conklin, "Lexico- graphical Treatment of Folk Taxonomies. " IJAL, 28:2, P a r t I V , April , 1962, pp. 119-137. He presents in a cube d iagram the "regular intersection of s ix components which comprise three simple oppositions. I ' See Thomas, 2.g. , for a comparison of three analyses of Ilocano pronouns, the third of which he recommends a s adequate for Ilocano.

8. The following allomorphs occur: In Set I , Is , ac~-*; 9occurs following consonants; occurs following vowels. In Set 11, Is , &-3; & o c c u r s following consonants; 3 occurs following vowels. In Set 11, 2s, mu -m; mu occurs following consonants; m occurs following vowels.

9. These mat r ices do not include a l l the intermediary experimental permutations that were made. Only those a r e shown f r o m which significant patterning developed.

10. These implications were discussed in Section 2.

11. Pike, 2.& , s ta tes , p. 21, "the single-celled formative may be called a n ideal particle.. . I '

12. Pike, "Language a s Par t i c le , Wave, and Field, " T h e Texas Quarterly, Vol. 11, No. 2, Summer , 1959, p. 38. "The view of language a s made up of field s e e s language a s functional, a s a

sys tem with par t s and c lasses of par t s so interrelated that no par t s 2ccur apar t i r o m their function in the total whole, which in turn occurs only a s the product of these par t s in functional relation to a meaningful social environment. "

13. Pike, Matr ix Permutat ion and Conflation, "The conven-tional simple morpheme of an inflectional type i s isomorphic with a formative which fills every ce l l of one raw of a mat r ix , o r of one column of a mat r ix (but not both). . .If we ca l l e i ther the full row o r a ful l column a vector pattern in the matr ix, then the simple inflection- a l morpheme i s a vector-patterned formative."

14. Pike, 3.s,Section I, C . , (7b) and (8).

15. The distribution of these two forrnatives can be phono- logically defined: -5occurs following a consonant; -2occurs following a vowel. This should not be interpreted to mean that there a r e no vowel c lus te rs i n the language.

17. Pike, "Dimensions of Grammat ica l Constructions," Language, 38: 221-44, 1962.

18. Matr ix Permutat ion &Conflation.

19. "Dimensions of Grammat ica l Constructions," p. 226.

You have printed the following article:

The Use of Matrix Technique in an Analysis of Atta Personal PronounsRuth Lusted; Claudia Whittle; Lawrence A. ReidOceanic Linguistics, Vol. 3, No. 1, Papers in Philippine Linguistics. (Summer, 1964), pp.138-160.Stable URL:

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Notes

17 Dimensions of Grammatical ConstructionsKenneth L. PikeLanguage, Vol. 38, No. 3, Part 1. (Jul. - Sep., 1962), pp. 221-244.Stable URL:

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