Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics

Treatment of Zero Pronouns in the Framework of
Lexical-Functional Grammar 1
Masanori Oya
Mejiro University
m.oya@mejiro.ac.jp

Abstract
This study presents both a Lexical-Functional Grammar (LFG) treatment and a typed-dependency grammar
treatment of zero pronouns in the Japanese language. Japanese uses elliptic sentences quite often, and theirfunctional-structural representation is problematic because they seem to violate the “completeness condition,”
which states that all the core arguments of a predicate must be present in its functional structure. This study
shows through a number of examples that this problem can be solved by positing the presence of zeropronouns with various semantic functions.

Keywords
Lexical-Functional Grammar, Dependency Grammar, Japanese, Zero Pronouns

1

Introduction

This study presents both a Lexical-Functional Grammar (LFG) treatment and a typed-dependency grammar
treatment of zero pronouns in the Japanese language. Japanese often uses elliptic2 sentences, that is,sentences in which nouns with core grammatical functions such as subject or object are absent (Kanatani
2002; Mikami 1972; Toyama 1973, among others). In terms of functional well-formedness (Kaplan &Bresnan 1982), elliptic sentences are problematic because their functional structure seems to violate thecompleteness constraint, which states that a predicate and all its arguments must be present in an f-structure(Kaplan & Bresnan 1982, p. 211–212).

Oya (2010) argued that such elliptic sentences contain zeropronouns that are the values of the core grammatical-function attributes, and that the completeness constraint
is in fact observed because of the presence of zero pronouns in the functional structures of these sentences.
In this study, we look at examples of Japanese sentences containing zero pronouns that belong to different
semantic types, and explain how the completeness constraint is observed in the functional structures for theseelliptic sentences.

2

Examples of Japanese elliptic sentences

It is often the case that Japanese sentences do not have subjects or objects.
1

Consider the following

This study is based on my presentation at the 18th Conference of Pan-Pacific Association of Applied Linguistics(PAAL) at Ajou University in Suwon, South Korea, August 19–20, 2013.
2
Actually, it will be argued later that they are not “elliptic” sentences, because they lack nothing. However, the terms“ellipsis” and “elliptic sentences” are used for a while in this section, in order to avoid misunderstanding.

1Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
dialogue.
(1)
Sarah: David, have you read this book?
David: Yes, I have.
Sarah: Is this interesting?
David: Yes, it is.
The natural spoken Japanese translation of this dialogue will be as follows in (2). Each sentence in (2) isfollowed by an English gloss in parentheses.
(2)Sarah: David, kono hon yonda?
(Sarah: David, this book read-past)
David: Un, yondayo.
(David: Yes read-past-ending)Sarah: Omoshiroi?
(Sarah: interesting)David: Un, omoshiroiyo.
(David: Yes interesting-ending)None of the sentences in (2) contains the subject. This fact, however, does not hinder native speakers ofJapanese from understanding these sentences, because it is obvious for them from the context who read what.
In this sense, native speakers of Japanese interpret sentences with more reference to the context than native
speakers of English, which requires the presence of pronouns.3

3Functional-structural representation of elliptic Japanese sentences

As indicated in Section 1, from the standpoint of Lexical-Functional Grammar, these elliptic sentences areproblematic because they do not appear to observe the completeness constraint, which states that a predicate
and all its arguments must be present in an f-structure (Kaplan & Bresnan 1982, p. 211–212). For example,
the sentence “(Un,) yondayo” in David’s first utterance in dialogue (2) above lacks both a subject and an
object.

Its functional structure would be like Figure 1 below.

This is not a well-formed functional

structure, because it violates the completeness constraint; values are missing for both the SUBJ attribute andthe OBJ attribute.

3

The Japanese language seems to reflect the high-context culture (Hall 1976) of Japanese people, while the English
language seems to reflect the low-context culture of many English-speaking peoples.

2

Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
PRED
SUBJ
OBJ
TENSE

'yonda<SUBJ, OBJ>'
[
]
[
]
PAST

Figure 1: The functional structure of “Yondayo.”
However, the fact that this sentence is natural for native speakers of Japanese with reference to a certain
mutually understood context suggests that the functional structure for an elliptic sentence such as “Yondayo”
is actually complete and there are no missing elements.
Oya (2010) argued that the presence of zero pronouns fills this gap. Zero pronouns are provided as partof lexical information, which is registered in the lexical entry for each verb. For example, the lexicalinformation for the verb yondayo is as follows. This lexical entry contains equations for both subject andobject zero pronouns.
(3)(↑PRED)= ‘yonda<SUBJ, OBJ>’(↑SUBJ PRED)=‘PRO’(↑SUBJ FORM)=ZERO(↑OBJ PRED)=‘PRO’(↑OBJ FORM)=ZERO(↑TENSE)=PAST(↑ENDING)=‘yo’4
The typed-dependency tree for the sentence “Yondayo” is shown below.
Root
ROOT
yondayo-1
PUNCT
'.'

Figure 2: The typed-dependency tree for “Yondayo.”
Dependency types for Japanese sentences in this study are based on de Marneffe and Manning (2012) andOya (2010). However, unlike in Oya (2010), case particles such as -ga, -wo, are all treated as postpositions,
not as subject case markers or object case markers. This policy is based on the claim that a given particle
functions not only as single case markers (Masuoka & Takubo 1992, p. 74).
The typed-dependency tree above is equivalent to the functional structure below.

Notice that thisfunctional structure contains both a subject zero pronoun and an object zero pronoun. These zero pronouns
ensure that this functional structure is complete.
4Here, -yo is a sentence-final particle by means of which the speaker asserts the meaning of the sentence to the listener(Ono & Nakagawa 1997).

3

Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
PRED
SUBJ

'yonda<SUBJ, OBJ>'
PRED
'PRO'
FORM
ZERO

OBJ

PRED
FORM

TENSE PAST
ENDING 'YO'
PUNCT FORM
ROOT

'PRO'
ZERO

'.'

ST MT -T YPEDECLARAT IVE

Figure 3: The functional structure for “Yondayo” with zero pronouns.
The zero pronouns contain no phonological features, and the context in which they are used determines theirantecedents, whether inter-clausally or intra-clausally5.

The word “inter-clausal” here means that theantecedent of a zero pronoun is found beyond the clause which contains this zero pronoun. In the sentence“Yondayo” in the dialogue (1) above, the antecedents of the zero pronouns are determined inter-clausally, or
deictically as the speaker and the book.
Overt core arguments depending on a verb, if any, can function as the intra-clausal antecedents of thezero pronouns of that verb. They also have the function of making explicit the meaning of the zeropronouns. Instances of intra-clausal antecedence of zero pronouns will be illustrated in the next section.

4

Semantic types of Japanese zero pronouns

Tomioka (2003, p. 324) claims that Japanese zero pronouns (null pronouns in his terms) have all thesemantic functions of English overt pronouns, as summarized below6:(4)(=(9) in Tomioka 2003, p. 324)
a. Referential
b. Bound variable
c. Unselectively bound variable
d. Pronouns with pronoun-containing antecedents
e. Indefinite pronouns
f. Property anaphoraThis section focuses on the typed-dependency tree representations of example sentences for each of thesesemantic functions of Japanese zero pronouns and on their equivalent functional-structural representations.
It will be shown that the differences between these semantic functions derive from the types of theantecedents of these pronouns and their scope of reference (inter- or intra-clausal).
4.1

Referential zero pronouns

Example (5) contains a referential zero pronoun (shown as PRO), which functions as the direct object of the5

Oya (2013) used the term “inter-sententially” and “intra-sententially,” yet these terms are misleading, because there
are instances where a sentence contains more than one clause and a zero pronoun in one of the clauses refers tosomething in another clause. Such instances should be called inter-clausal reference.
6
Along with these functions, deictic usage of zero pronouns must also be taken into consideration. Deictic zeropronouns refer to the participants in the discourse, such as the speaker or the hearer (Kim, Park, Song, Park, and Lee
2010 , p.115). In this sense, deictic zero pronouns are subtypes of referential zero pronouns.

4Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
verb “sasotta” ‘invited’. The second sentence has two interpretations: one is that Sarah also invited John;
the other is that John also invited David. This ambiguity is due to the fact that a noun with the focus marker-mo can express either the subject of the object of a verb, while the zero pronoun in the second sentence canrefer to either the subject or the object of the first sentence. The reader/listener of this sentence must thenjudge whom this zero pronoun refers to, with reference to the context where it is uttered.
(5)
Sarah-wa

David-wosasoi,John-moSarah-topic

David-postp

invite-past-advcl John-focusPROsasot-ta.

PRO

invite- past

“Sarah invited David, and she also invited John.” or “Sarah invited David, and John also invited him.”
The typed-dependency tree for the sentence above is shown below. Notice that there is no node for PRO.
This is because this PRO is registered in the lexical entry of the verb “sasotta.”
Root-0ROOT
sasotta
ADVCL
FOCUS
John-mo

sasoi

PUNCT
.

TOPIC
Sarah-wa

POSTP_woDavid-wo

PUNCT,

Figure 4: The typed-dependency tree for “Sarahwa Davidwo sasoi, Johnmo sasotta.” (meaning: “Sarah
invited David, and she also invited John.” Or, “Sarah invited David, and John also invited him.”)
The typed-dependency tree above is equivalent to the functional structure below. Notice which elements
the indices “i,” “j,” and “k” are assigned to in the structure. The subject zero pronoun of the verb “sasotta”
in the functional structure for the second clause refers to “Sarah” (assigned the index “i”), while the object
zero pronoun of the same verb refers to “John” (assigned “k”); therefore, the second clause means that Sarah
invited John.

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Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
PRED'sasotta<SUBJ, OBJ>'

SUBJ

PRED

'PROi'

FORM

ZERO

OBJ

FOCUS

PRED

'PROk'

FORM

ZERO

PRED

'Johnk'PRED
SUBJ'sasotta<SUBJ, OBJ>'
PRED'PROi'
FORM
ZERO

OBJ

PRED
FORM

'PROj'
ZERO

TOPIC

PRED

'Sarahi'

POSTP_wo PRED

'Davidj'

TENSE
PUNCT
ADVCL
TENSE
PUNCT
ROOT

PAST
FORM

','

STMT-TYP E

DECLARATIVE

PAST
FORM

'.'

STMT-TYP E

DECLARATIVE

Figure 5: The functional structure for “Sarahwa Davidwo sasoi, Johnmo sasotta.” (meaning: “Sarah invited
David, and she also invited John.”)
The following functional structure is also equivalent to the typed-dependency tree in Figure 4 above, yet it
has a different semantic interpretation. Notice how the indices “i,” “j,” and “k” are assigned differently
from those in the previous functional structure. The subject zero pronoun of the verb “sasotta” in thesecond clause refers to “John” and the object zero pronoun of the same verb refers to “David”; therefore, thesecond sentence means that John invited David.

6Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
PRED'sasotta<SUBJ, OBJ>'

SUBJ

PRED

'PROk'

FORM

ZERO

OBJ

FOCUS

PRED

'PROj'

FORM

ZERO

PRED

'Johnk'PRED
SUBJ'sasotta<SUBJ, OBJ>'
PRED'PROi'
FORM
ZERO

OBJ

PRED
FORM

'PROj'
ZERO

TOPIC

PRED

'Sarahi'

POSTP_wo PRED

'Davidj'

TENSE
PUNCT
ADVCL
TENSE
PUNCT
ROOT

PAST
FORM

','

STMT-TYP E

DECLARATIVE

PAST
FORM

'.'

STMT-TYP E

DECLARATIVE

Figure 6: The functional structure for “Sarahwa Davidwo sasoi, Johnmo sasotta.” (meaning: “Sarah invited
David, and John also invited him.”)
As we have seen in the functional structures above, either subject or object zero pronouns can refer to thenoun “John” intra-clausally. In both cases, the antecedents of zero pronouns of this type are referential.
4.2

Bound variables

Example (6) contains a zero pronoun as a bound variable functioning as the subject of the verb “okorareta”‘was scolded’. The construction “dono ~ mo” means ‘every ~’ if the sentence is affirmative, or ‘no ~’ if thesentence is negative.
(6)
Dono

gakusei-moSarah-niPROokorare-ta-to

it-ta.

Which

student-focus

Sarah-postp

PRO

be.scolded.at-past-ccomp

say-past“Every student said that he or she was scolded by Sarah.”
The typed-dependency tree for the sentence above is shown below.
Root

itta
FOCUS

PUNCT
CCOMP

gakusei-moDETokorareta-to
POSTP_nidonoSarah-ni7.

Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
Figure 7: The typed-dependency tree for “Dono gakuseimo Sarahni okoraretato itta.” (“Every student said
that he or she was scolded by Sarah.”)
The typed-dependency tree above is equivalent to the functional structure below. The index “i” is assigned
to the subject zero pronoun “itta” ‘said’, the subject zero pronoun “okorareta” ‘be scolded’, and the local
functional structure, which is the value of the attribute FOCUS. The noun “gakusei” ‘student(s)’ with thefocus marker “-mo” is modified by an interrogative determiner “dono,” and this construction means ‘every
student’, as mentioned before. Therefore, the zero pronouns with the index “i” in the functional structure
below refer to the every student.
PRED
SUBJ

'itta<SUBJ, CCOMP>'PRED'PROi'FORM
ZERO

CCOMP PRED
SUBJ

'okorareta<SUBJ>'PRED'PROi'TYPE
ZERO

POSTP_ni PRED
'Sarah'
TENSE
PAST
VOICE
PASSIVE
FOCUS

TENSE
PUNCT
ROOT

PRED
DET

'gakusei'
FORM
TYPE

'dono'
INTERROGATIVE

PAST
FORM

'.'

ST MT -T YPEDECLARAT IVEi

Figure 8: The functional structure for “Dono gakuseimo Sarahni okoraretato itta.” (“Every student said thathe or she was scolded by Sarah.”)This example suggests that zero pronouns as bound variables refer to their antecedents intra-clausally.
4.3

Unselectively bound variables

Unselectively bound variables are those whose antecedents are not referential, and they appear beyond thescope of their antecedents (Tomioka 2003, p. 322); in other words, zero pronouns of this type refer to adefinite entity, while their antecedents refer to an indefinite entity.

They refer to their antecedents

inter-clausally. For more detail of this type of pronouns, see Heim (1990). Example (7) contains a zeropronoun as an unselectively bound variable.
(7)
Sarah-wa

David-niatarashii

hon-wokat-ta-ga,

Sarah-topic

David-postp

new

book-postp

buy-past-advcl,

David-wasuguniPRO

nakushi-ta.

David-topic

immediatelyPROlose-past“Sarah had bought a new book for David, but he immediately lost it (the new book that Sarah bought).”
The typed-dependency tree for the sentence above is shown in the figure below.
8Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics

Rootnakushi-ta
ADVCL
kat-ta-ga
TOPIC
Sarah-wa

PUNCT
ADVMODsuguni.

TOPIC
David-wa

PUNCT
POSTP_wo
POSTP_ni,
David-ni
hon-woAMOD
atarashii

Figure 9: The typed-dependency tree for “Sarahwa Davidni atarashii honwo kattaga, Davidwa suguni
nakushita.” (“Sarah had bought a new book for David, but he immediately lost it.”)
The typed-dependency tree above is equivalent to the functional structure below. Notice how the indices “i,”“j,” and “k” are assigned.
PRED
SUBJ

'nakushita<SUBJ, DOBJ>'
PRED'PROk'
FORM
ZERO

DOBJ

PRED
FORM

'PROj"
ZERO

ADVCL

PRED
SUBJ

'katta<SUBJ,OBJ>'
PRED'PROi'
TYPE
ZERO

OBJ

PRED
TYPE

'PROj'
ZERO

TOPIC

PRED

'Sarahi'

POSTP_ni

PRED'Davidk'

POSTP_wo PRED
AMOD

'hon'
PRED

TENSE

PAST

PRED

'Davidk'

ADVMOD PRED

'suguni'

TOPIC

ROOT

TENSE

PAST

PUNCT

FORM

'.'

ST MT -T YPEDECLARAT IVE'atarashii'j

Figure 10: The functional structure for “Sarahwa Davidni atarashii honwo kattaga, Davidwa suguni
nakushita.”
The example above suggests that Japanese zero pronouns, as unselectively bound variables, refer to theirantecedents inter-clausally, and that their antecedents themselves are not referential.
4.3

Pronouns with a pronominal-containing antecedent

Example (8) contains a zero pronoun with a pronominal-containing antecedent.
(8)9Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
Sarah-wajibun-noie-wo

ut-ta-shi,

Sarah-topic

self-postp

house-postp

sell-past-advcl

David-moPRO

ut-ta.

David-focusPROsell-past“Sarah sold her own house, and David also sold his own.”
Root
ROOT
ADVCL
uttashi

FOCUS
David-moTOPIC
Sarah-wa

POSTP_wo
ie-wo
POSTP_no

utta
PUNCT
.

PUNCT
,

jibun-noFigure 11: The typed-dependency tree for “Sarahwa jibunno iewo uttashi, Davidmo utta.”(“Sarah sold her
own house, and David also sold his own.”)
The typed-dependency tree above is equivalent to the functional structure below. Notice that the index “i”
is assigned to the subject zero pronoun of the verb “utta” ‘sold’ in the first clause, and the topic “Sarah” inthe first clause. In contrast, the index “j” is assigned to the local functional structure that is the value of theattribute POSTP_wo (“jibun-no ie”, not just “ie”), and the object zero pronoun of the verb “utta” in thesecond clause.
Notice that the reflexive pronoun “jibun,” which is the value of the attribute POSTP_no, cannot be
assigned a unique index. This reflexive pronoun refers to ‘Sarah’ in the first clause; hence, it should beindexed “i”. On the other hand, the local functional structure containing this reflexive pronoun is referred
to by the object zero pronoun in the second clause. Then, the reflexive pronoun comes to refer to thesubject zero pronoun, which refers to ‘David’; hence, it should be indexed “k.” For the binding of reflexive
pronouns with respect to the notion of f-structure nucleus, see Bresnan (2001, p.215).

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Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
PRED
SUBJ

'utta<SUBJ,OBJ>'
PRED'PROk'
TYPE
ZERO

OBJ

PRED
TYPE

'PROj'
ZERO

FOCUS

PRED

'Davidk'

PRED
SUBJ

'utta<SUBJ,OBJ>'
PRED'PROi'
TYPE
ZERO

OBJ

PRED
TYPE

'PROj'
ZERO

TOPIC

PRED

'Sarahi'

POSTP_wo PRED

'ie'
PRED

'PRO'

FORM
TYPE

'jibun'
REFLEXIVEPOSTP_no

TENSE
PUNCT
ADVCL
TENSE PASTPUNCT FORM
ROOT

PAST
FORM

j

','

ST MT -T YPEDECLARAT IVE'.'

ST MT -T YPEDECLARAT IVE

Figure 12: The functional structure for “Sarawa jibunno iewo uttashi, Davidmo utta.”
4.4

Indefinite pronouns

Example (9) contains a zero pronoun as an indefinite pronoun.
(9)
Sarah-wakuruma-wo

ut-ta-shi,

David-moPRO

ut-ta.

Sarah-topic

car-postp

sell-past-advcl

David-focusPROsell-past“Sarah sold a car, and David also sold one.”
Root
ROOT
utta
ADVCL
FOCUS
Davidmouttashi

PUNCT
.

TOPIC
Sarah-wa

POSTP_wokuruma-wo

PUNCT,

Figure 13: The typed-dependency tree for “Sarahwa kurumawo uttashi, Davidmo utta.” (“Sarah sold a car,and David also sold one.”)
The typed-dependency tree above is equivalent to the functional structure below. Notice that the index forthe object zero pronoun in the first instance of “utta” is different from that for the object zero pronoun in thesecond. This is because the car that Sarah sold cannot be the same car that David sold, and therefore theobject zero pronoun of the first sentence refers to something different from the referent of the object zeropronoun in the second sentence. That is, the object zero pronoun refers to something external to thesentence whose identity can be interpreted according to the context.

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Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
PRED
SUBJ

'utta<SUBJ,OBJ>'
PRED'PROk'
TYPE
ZERO

OBJ

PRED
TYPE

'PRO'
ZERO

FOCUS

PRED

'Davidk'

PRED
SUBJ

'utta<SUBJ,OBJ>'
PRED'PROi'
TYPE
ZERO

OBJ

PRED
TYPE

'PROj'
ZERO

TOPIC

PRED

'Sarahi'

POSTP_wo PRED

'kurumaj'

TENSE
PUNCT

PAST
FORM

','

STMT-TYP E

DECLARAT IVE

ADVCL
PUNCT
ROOT

FORM

'.'

STMT-TYP E

DECLARATIVE

Figure 14: The functional structure for “Sarawa kurumawo uttashi, Davidmo utta.”
4.5

Property anaphora

Example (10) contains a zero pronoun as a property anaphor. The construction ~shika V-nai means ‘doonly ~’; issatsu-shika yoma-nai means ‘read only one book.’(10)
Sarah-wa

shuu-nisan-satsu

hon-woyomu-ga,Sarah-topic

week-postp

three-books

book-postp

read-advcl,

David-wa

issatsu-shikayoma-nai.

David-topic

one.book-focus

read-neg‘Sarah reads three books a week, but David reads only one book (a week).’RootyomanaiADVCL
yomu-ga
TOPIC
Sarah-wa

PUNCT

TOPIC
David-wa

POSTP_wo
ADVMODsansatsu
hon-woPOSTP_ni

FOCUS
issatsushika

.

PUNCT
,

shuuniFigure 15: The typed-dependency tree for “Sarawa shuuni sansatsu honwo yomuga, Davidwa issatsushika
yomanai.”

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Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
The typed-dependency tree above is equivalent to the functional structure below. The index “j” is assigned
to the object zero pronoun of the verb “yomu” in the adverbial clause, and the word “hon,” which is thevalue of the POSTP_wo attribute. The index “j,” however, is not assigned to the object zero pronoun of theverb “yomanai.” This is because this sentence does not make explicit whether Sarah and David read thesame book.
PRED
SUBJ

'yomanai<SUBJ, DOBJ>'
PRED'PROk'
FORM
ZERO

DOBJ

PRED
FORM

'PRO'
ZERO

ADVCL

PRED
SUBJ

'yomu<SUBJ,OBJ>'
PRED'PROi'
TYPE
ZERO

OBJ

PRED
TYPE

TOPIC

PRED

'Sarahi'

ADVMODPRED
POSTP_ni'sansatsu'
PRED'shuuni'

POSTP_wo PREDTENSE
PRESENTROOT'PROj'
ZERO

TOPIC

PRED

'Davidk'

FOCUS
TENSE
NEG
PUNCT

PRED
PAST
+
FORM

'issatsu''.'

ST MT -T YPEDECLARAT IVE'honj'

Figure 16: The functional structure for “Sarahwa shuuni sansatsu honwo yomuga, Davidwa issatsushika
yomanai.”
It seems that Japanese zero pronouns of this type refer to numeral classifiers (“issatsu” or “one book” and“sansatsu” or “three books” in the example above) intra-clausally. What is at issue here, however, is theidentity of the antecedent of the object zero pronoun of “yomuga” in the first part of this sentence. In
principle, this can refer to “sansatsu,” along with “honwo.”

However, it is safe to consider that a zeropronoun cannot refer to more than one antecedent. In addition to this, it is natural to consider that a zeropronoun refers to an entity, if any (in this example, “hon(-wo),” meaning “books in general”), rather than anumeral classifier.

5

Conclusion

This study presented both a Lexical-Functional Grammar (LFG) treatment and a typed-dependency grammar
treatment of zero pronouns in the Japanese language. We showed that the completeness constraint isobserved in the functional structures for these “elliptic” sentences, which contain zero pronouns of different
semantic types.
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Selected Papers of the 18th Conference of Pan-Pan Pacific Association of Applied Linguistics
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