Annotating Japanese Numeral Expressions
for a Logical and Pragmatic Inference Dataset
Kana Koyano1 , Hitomi Yanaka2 , Koji Mineshima3 , Daisuke Bekki1
1Ochanomizu University, 2 The University of Tokyo, 3 Keio University{2-1-1 Otsuka, Bunkyo-ku; 7-3-1, Hongo, Bunkyo-ku; 2-15-45, Mita, Minato-ku}, Tokyo, Japan{koyano.kana, bekki}@is.ocha.ac.jp, hyanaka@is.s.u-tokyo.ac.jp, minesima@abelard.flet.keio.ac.jp

Abstract
Numeral expressions in Japanese are characterized by the flexibility of quantifier positions and the variety of numeralsuffixes. However, little work has been done to build annotated corpora focusing on these features and datasets for testing theunderstanding of Japanese numeral expressions. In this study, we build a corpus that annotates each numeral expression in anexisting phrase structure-based Japanese treebank with its usage and numeral suffix types. We also construct an inference test
set for numerical expressions based on this annotated corpus. In this test set, we particularly pay attention to inferences where
the correct label differs between logical entailment and implicature and those contexts such as negations and conditionals
where the entailment labels can be reversed. The baseline experiment with Japanese BERT models shows that our inference
test set poses challenges for inference involving various types of numeral expressions.
Keywords: numeral expressions, Japanese, natural language inference, entailment, implicature

1.

Introduction

For example, the English sentence “There are three students” can be expressed in Japanese at least in the following three ways.
(1)

学生が
3人
いる
Gakusei-ga san-nin iru
student(s)-NOM three-CLS be-PRS

ences correspond to entailment and implicature, whichhave been discussed in the linguistic literature (Levinson, 1983; Horn, 1989; Levinson, 2000). For example,
consider the following premise–hypothesis pair.
(4)

男性が 道端に4人 座って いた
Dansei-ga mitibata-ni yo-nin suwatte ita
men-NOM street-LOC four-CLS sit-PROG bePST‘Four men were sitting on the street.’(5)

男性が 道端に5人 座って いた
Dansei-ga mitibata-ni go-nin suwatte ita
men-NOM street-LOC five-CLS sit-PROG bePST‘Five men were sitting on the street.’‘There are three students.’
(2)

3人の
学生が
いる
San-nin-no gakusei-ga iru
three-CLS-GEN student(s)-NOM be-PRS‘There are three students.’

(3)

3名の
学生が
いる
San-mei-no gakusei-ga iru
three-CLS-GEN student(s)-NOM be-PRS‘There are three students.’

In (1) and (2), “3人” (three people) appears in different
positions.
In (2) and (3), the suffix (i.e. classifier) for person isdifferent (“3人” and “3名,” respectively). The varietyof quantifier positions and numeral suffixes is an important feature of the Japanese language. However, little work has been done to build a corpus focusing onthese features or a dataset to test the understanding ofJapanese numeral expressions.
Natural Language Inference (NLI) is the semantic taskof determining whether the hypothesis is true, false, orneither, when the premises are all true. It is considered
one of the core knowledge underlying natural language
understanding. Recently, not only semantic modes ofreasoning, but also pragmatic modes of reasoning havebeen explored in the field of natural language processing (Jeretic et al., 2020). These two modes of infer-

We use different labels (logical label and pragmatic
label) for the judgments based on entailment and implicature, respectively, because they may differ on thesame premise–hypothesis pair: the logical label for thisinference is NEUTRAL, whereas the pragmatic label is
CONTRADICTION . The latter is so because, along with
Grice’s maxim of quantity, if the speaker knew that fivepeople were sitting there, they would say so, and thefact that they dared to say (4) implies that there is nofifth person. In other words, in entailment, inferences
are made only from the semantic information containedin the premises and hypothesis. In implicature, however, the assumption that normal conversation proceeds
according to the co-operative principle gives rise to information not semantically included in the utterance,
considering the context and the speaker’s intention, as
suggested in Grice’s maxims of conversation (Levinson, 1983; Grice, 1989).
In this study, we construct a Japanese corpus in which
numeral expressions are annotated regarding the classi-

fication of syntactic patterns and the usage of numeral
expressions. We use sentences containing numeral expressions extracted from the NINJAL Parsed Corpus ofModern Japanese (NPCMJ) (NINJAL, 2016), which isa phrase structure-based treebank for Japanese. Furthermore, we construct an inference test set for numeral expressions based on this corpus, which reports
two modes of judgments, entailment and implicaturefor each premises-hypothesis pair.
In this paper, we report on the design of the corpus andinference test set as well as the evaluation results of abaseline experiment. The constructed dataset will bemade publicly available in a research-usable format1 .

2.

Related WorkRegarding the study of NLI focusing on English numeral expressions, (Naik et al., 2018) presents an inference dataset that contains 7,596 premise–hypothesis
pairs, with 2,532 in each gold label (entailment, neutral, and contradiction). However, a recent study (Liu etal., 2019) has pointed out that the majority of problems(about 82% of the total) in this dataset can be solved
using a few heuristic rules, which is due to the fact thatthe inference of numeral expressions is constructed using a simple template.
Jeretic et al. (2020) provided an English NLI datasetthat focuses on the distinction between logical entailment, presupposition, and implicature. It also contains
inference problems for scalar implicature triggered bynumeral expressions. However, it is automatically constructed from templates and thus the sentences are relatively simple.
Cui et al. (2022) examined the extent to which multilingual pre-trained language models capture the behavior of generalized quantifiers including various typesof numeral expressions in English. Their experiments
showed that quantifiers cause performance drops for
NLI and question answering models. We can say thatnumeral expressions pose an important challenge to thestudy of NLI and other tasks for natural language understanding. Our corpus and inference dataset focusing
on numeral expressions in Japanese contribute further
insight on how pre-trained language models work.
Previous Japanese inference datasets include
JSeM (Kawazoe et al., 2017), the formal semantics test set (the Japanese version of FraCaS);JSNLI (Yoshikoshi et al., 2020), the Japaneseversion of English SNLI (Bowman et al., 2015);
JSICK (Yanaka and Mineshima, 2021b), the Japaneseversion of English SICK(Marelli et al., 2014); anda crowdsourced dataset from real text, reputation, a
travel information website (Hayashibe, 2020), andother sources. However, in these datasets, the syntactic
and semantic diversity of Japanese numeral expressions is not fully taken into account. Narisawa et al.
(2013) investigated cases where numeral expressions
1
https://github.com/KanaKoyano/numeral-expressionscorpus

are problematic in Japanese NLI and implemented a
module for normalizing numeral expressions. They
classify premise–hypothesis pairs containing numeral
expressions into seven categories and describe theprocess required to correctly determine the entailment
relation, but they do not consider the difference
between the two inference types (namely, entailment
and implicature), which may give rise to different
judgements according to the classification of numeral
expressions and numeral suffixes.
Given these considerations, in our study, we first annotate numeral expressions in a Japanese corpus containing real Japanese texts and classify them according
to their usages and the difference in numeral suffixes.
By using the annotated corpus, we create an inference
dataset involving numeral expressions annotated withentailment and implicature labels.

3.
3.1.

Syntax and Semantics of JapaneseNumeral Expressions
Classification of numeral suffixes

According to Iida (2021), numeral suffixes are classified into three categories: sortal suffixes, unit-forming
suffixes, and measure suffixes. In addition, some words
have an ordinal number suffix (Okutsu, 1996), which
expresses order within a time line or sequence. Thus,in this study, we propose a taxonomy that extends thethree types of numeral suffixes in Iida (2021) with ordinal number suffix. Examples of each type of numeralsuffix are shown in Table 1.
Table 1: Examples and the number of occurrences ofeach type of numeral suffix
Type

Examplesortal suffixes
unit-forming suffixes
measure suffixes
ordinal number suffixes

人, 頭, 冊, 枚
瓶, 箱, 袋, パック, 切れ
リットル, 円, バイト
月, 日, 番, 位Occurrence
56
13
74
107

The classification of some numeral suffixes is notuniquely determined by their surface forms but depends
on the context and usage. For example, “階” (floor) in“会議室は建物の3階にある” (the conference room ison the third floor of the building) is an ordinal number
suffix, while “階” (floor) in “ここから3階のぼったところに会議室がある” (there is a conference room
three floors up from here) is a measure suffix. The former refers to a specific location of the conference room,
while the latter refers to the number of floors to go up.
Note that, in the latter, the conference room is not necessarily located on the third floor.

3.2.

Position of occurrence of numeral
expressions

Encyclopedia of Japanese (EJ) (Yazawa, 1988) classified the syntactic patterns containing numeral expressions into four categories: Q no NC, N no QC, NCQ,
and NQC, where Q, N, C stand for a numeral together

with a classifier, a common noun, and a case marker,
respectively. Iwata (2013) added two categories to theclassification of EJ, predicate type and De type. In thisstudy, we extended the classification by adding the following types, the examples of which are shown in Table
2.

Table 3: Example and the number of occurrences ofeach usage of numeral expression
Type

ExampleQ represents the category information of N

3人の学生
(three students)
5人の集団(a group of 5 people)
集団の1人(one person from the group)
50歳の男性(50 years old man)
2回来る
(come twice)
3日滞在する(stay for 3 days)
9時に来る(come at 9:00)
2%上昇する(increase by 2%)
渡航歴は2回(two trips)
1人暮らし(living alone)

Q represents the number of elements that constitutes N
Q represents part of the elements that constitutes N
Q represents an attribute or characteristic of N

QV: Q semantically modifies the verb V.

Q for the number of times V has taken place
Q for the period in which V took place

NvCQ: Q is a predicate on the event noun phrase Nv.
N dropout: The so-called pronominal usage in which
no N of Q no NC is omitted.

Q representing the time that V took place
Q for characteristics of V
Q to qualify Nv
idiom

QtQ: A time expression and a numeral expression are
adjacent, such as in “1時間(で)500円” (500 yen
for 1 hour) and “1ヶ月に1回” (once a month).
idiom: Idiomatic and conventional usages.

Occurrence

Table 4: Occurrences of upward/downward monotone
inference
upward monotone downward monotone
1173
118

(Q): A numeral expression enclosed within a bracket.

Table 2: Example and the number of occurrences ofeach position of numeral expressions
Type

ExampleQ no NC
N no QC
NCQ
NQC
predicate
De
QV
NvCQ
N dropout
QtQ
idiom
(Q)

3人の学生が来た
学生の3人が来た
学生が3人来た
学生3人が来た
来た学生は3人だ
学生が3人で来た
東京に3回行った
渡米したことは2回ある
3人はお金を払った
1時間500円かかる
1人暮らし, 8人兄弟
（1998年）

3.3.

Occurrences
31
11
53
11
1
7
74
6
24
3
14
15

Usage of numeral expressions

In addition to the usage of the numeral expression Q
studied by Iwata (2013), the present study adds three
new usage categories of Q by modifying the noun N
and four more usage categories of Q by modifying theverb V. In addition, we add the usage of the expression
Q by modifying Nv and idiomatic usage. In summary,we classify each numeral expression according to ten
usage categories. The usage classifications and their
examples are shown in Table 3.

4.

Semantic Annotation of Numeral
Expressions

In this study, 250 numeral expressions of sentences extracted from the NPCMJ were annotated by a graduate
student with a background in linguistics.

Semantic annotation We assigned <num> tags to
the numeral expressions that appeared in sentences, andmade annotations for the classification of numeral suffixes, position of occurrence, and usage of numeral expression, as described in Section 3. When multiple numeral expressions appeared in a sentence, we marked
the target expression with the <num> tag. The numberof occurrences of each type of numeral suffixes, eachposition of numeral expression, and each usage in the
corpus are shown in Table 1, Table 2, and Table 3, respectively.

5.
5.1.

Inference Test Set of Numeral
Expressions

Data creation

We create an inference test set from a corpus of numeral expressions. We use each sentence in the corpus
for a premise sentence T . The hypothesis sentence wascreated using the sentence annotated in Section 4. We
select the clause that does not change the meaning of
the numeral expression tagged with <num> as in (6),change the numeral, and add a quantifier modifier, asin (7).
(6)

仙台都市圏（広域行政圏）のSendai-tosi-ken（Kouiki-gyousei-ken）-no
推計人口は約<num>151万人</num>suikei-zinkoo-wa yaku-151man-nin
で. . .
de. . .
Sendai-metropolitan-area(greateradministrative-area)-GEN
estimatedpopulation-NOM approximately-1.51-millionCLS be-cont‘The estimated population of the Sendai
metropolitan area (greater administrative area)

60
8
7
64
1
21
57
13
5
14

Table 5: Examples of the inference test set
gold labels
premise T and hypotheses H− and H+
logical(T , H− )pragmatic(T , H+ )pragmatic

logicalT : 前回１９９７年の税率アップ時を参考にすれば、昨年１２月～３月の駆け込み需要で前年比１％の売り上げ増が見込まれる半面、ことし４月以降は４～５％程度の落ち込みが予想される(If the previous tax rate increase in 1997 is used as a reference, a 1% year-on-year increase in sales is expectedfrom December to March of last year due to rush demand, while a 4-5% decline is expected from April of this year.)H− : 前回の税率アップは１９９６年より後だった

ENTAILMENTENTAILMENTCONTRADICTIONCONTRADICTION

NEUTRAL

NEUTRALENTAILMENTENTAILMENT

NEUTRAL

NEUTRALENTAILMENTENTAILMENT(The last tax rate increase was later than 1996.)

H+ : 前回の税率アップは１９９８年より後だった(The last tax rate increase was later than 1998.)

T : 勿論、私ひとりで四升呑みほしたわけでは無い(Of course, I didn’t finish all four bottles by myself.)

H− : 勿論、私ひとりで三升以上呑みほしたわけでは無い(Of course, I didn’t finish more than three bottles by myself.)

H+ : 勿論、私ひとりで五升以上呑みほしたわけでは無い(Of course, I didn’t finish more than five bottles by myself.)

T : あの頃は、100ドルを円に両替すれば、12000円になりました(Back then, if you exchanged $100 into yen, it became 12,000 yen.)H− : あの頃は、50ドル以上を円に両替すれば、12000円になりました(Back then, if you exchanged more than $50 into yen, it became 12,000 yen.)

H+ : あの頃は、150ドル以上を円に両替すれば、12000円になりました(Back then, if you exchanged more than $150 into yen, it became 12,000 yen.)

Table 6: Results of baseline experiments using Japanese BERT (accuracies of correct responses)
training

logical label
all
ENTAILMENT

JSICK
JSNLI

32.22%
41.21%

CONTRADICTION

NEUTRAL

10.61%
35.52%

17.74%
5.66%

70.83%
70.83%

Table 7: Inference test set statistics
logical label
pragmatic label

ENTAILMENTCONTRADICTION

NEUTRAL

432
433

594
738

165
120

is approximately 1.51 million, and . . . ’(7)

仙台都市圏の推計人口はSendai-tosi-ken-no suikei-zinkoo-wa
160万人
以上 である160man-nin izyoo dearu
Sendai-metropolitan-area-GEN
estimatedpopulation-NOM
1.6-million-CLS
over
be-PRS‘The estimated population of the Sendai
metropolitan area is over 1.6 million’

We rephrase numerals in a premise sentence T withboth a lower number (H− ) and a higher number (H+ )and create two premise–hypothesis pairs (T , H− ) and(T , H+ ) from T .
As in (6), when a modifier such as “約” (approximately) is added to a numeral expression, all judgment
labels would become NEUTRAL if the hypothesis sentence is created with too small a number. In such cases,
the numbers in a hypothesis sentence were modified
so that the pragmatic label becomes as CONTRADIC TION while preserving its naturalness. In cases where
adding a modifier would result in making an unnatural sentence as in (7), we changed the word order of asentence while maintaining its original meaning in creating a hypothesis sentence.
In this study, we did not use sentences involving idiomatic usage because changing the number or adding
a modifier of such sentences would make the rephrased

pragmatic label
all
ENTAILMENT
30.83%
44.46%

CONTRADICTION

70.90%
70.67%

9.62%
35.23%NEUTRAL

16.67%
6.67%

sentences unnatural.

5.2.

Monotonicity inference

We also create inference problems involving the socalled monotonicity inference triggered by numeral expressions. If M is a more specific concept (subconcept) of N , then a sentence φ(M ) involving M usuallyentails a sentence φ(N ) involving N . We call suchinference upward monotone inference. In the case ofnumeral expressions, for example, “200人” (200 people) refers to a subconcept of “100人” (100 people),so if the sentence There are 200 people in the hall istrue, then the sentence There are 100 people in the hallis also true. However, if numeral expressions are embedded in downward monotonic contexts such as negations and conditionals, the entailment relation is inverted. Here a sentence containing the more general
concept φ(N ) entails a sentence containing a more specific concept φ(M ). For example, the sentence There
were not 100 people in the hall entails the sentence
There were not 200 people in the hall.
The first example in Table 5 is a premise-hypothesis
pair in an upward monotone context. The second andthird examples are premise-hypothesis pairs in a downward monotone context involving negation and conditionals, respectively. Table 4 shows the number ofoccurrences of upward and downward monotone inference. At present, the number of downward monotone
inference is small, reflecting the fact that expressions
that trigger this type of inference is rare in the corpus.
It is left for future work to annotate more examples of
downward monotone inferences involving numeral expressions.

5.3.

Inference test set

The inference test set created in this study contains
1,291 premise–hypothesis pairs. One annotator assigned logical (entailment) and pragmatic (implicature)labels to each pair in the inference test set.
The statistics of the inference test set are shown in
Table 7 and examples of premise and hypothesis sentences are shown in Table 5. We can see that the numbers of CONTRADICTION and NEUTRAL judgments forlogical and pragmatic labels are different because someof those that are NEUTRAL for logical labels are CON TRADICTION for pragmatic labels.

5.4.

Baseline experiments

To evaluate the extent to which current standard pretrained language models can handle inferences that
require an understanding of numeral expressions, we
conducted an evaluation experiment using Japanese
BERT (Devlin et al., 2019) as a baseline model. In
the experiment, we used two standard Japanese NLI
datasets to finetune BERT models on the NLI task:
Japanese SICK datasets (JSICK, 5,000 pairs) (Yanaka
and Mineshima, 2021a) and Japanese SNLI datasets(JSNLI, 530,000 pairs) (Yoshikoshi et al., 2020).
Table 6 shows the evaluation results of the NLI model.
Overall, the accuracies to the Japanese BERT tend tobe higher for models trained on JSNLI than for thosetrained on JSICK, but both were below 50%. In particular, the accuracy for ENTAILMENT was over 60%,
while the accuracies for CONTRADICTION and NEU TRAL were both below 40%, suggesting a tendency to
predict ENTAILMENT when the model is trained on an
existing dataset. As for the difference in training data,
the accuracy for CONTRADICTION was higher for both
logical label and pragmatic label when JSNLI was usedthan when JSICK was used, which might be due to thelarger number of training data used for JSNLI.
Table 8 shows the accuracies for each position of occurrence of the numeral expressions. The results showthat the performance on inference examples involving
numeral expressions of De types was low. One possible reason for the low performance is that numeral expressions of De types might be not frequently appear
in general, including the training data. Thus models
struggled with predicting correct labels for inferences
involving numeral expressions of De types.

6.

Conclusion

In this study, we constructed a Japanese corpus of numeral expressions as well as semantic annotations including the classification of numeral suffixes and theirusage. We also created a logical and pragmatic inference test set from the corpus of numeral expressions.
As a baseline experiment, we evaluated Japanese BERT
on our inference test set. The experiment showedthat our inference test set for numeral expressions constructed is challenging enough for the current standard
NLI models. When constructing the annotated corpus

Table 8: Accuracies for each position of occurrenceType
Q no NC
N no QC
NCQ
NQC
predicate
De
QV
NvCQ
N dropout
QtQ(Q)

logical label
JSICK
JSNLI
29.70% 35.76%
28.79% 40.91%
32.00% 44.33%
31.82% 48.48%
0.00% 25.00%
28.21% 43.59%
32.39% 39.95%
27.27% 59.09%
39.23% 38.46%
33.33% 33.33%
34.43% 42.62%

pragmatic label
JSICK
JSNLI
24.85% 36.97%
25.76% 39.39%
31.00% 48.33%
33.33% 53.03%
0.00% 25.00%
23.08% 41.03%
33.10% 44.68%
27.27% 45.45%
36.92% 45.38%
20.00% 40.00%
31.15% 42.62%

for numeral expressions and the inference dataset, we
focused on the characteristics of Japanese, such as theflexibility of quantifier positions and the diversity ofnumeral suffixes. Future work remains to annotate andanalyze more semantically complex phenomena, i.e.,
those phenomena that have been studied in the previous analysis of quantification in English (Bunt, 2020),
including the scope of quantification, definiteness, andthe distributive/collective distinction in Japanese numeral expressions. We will also continue to expand
our numeral expression corpus and inference dataset aswell as analyze the current NLI models on our inference dataset.

Acknowledgments
We thank the five anonymous reviewers for their helpful comments and feedback. This work was partially supported by JST CREST Grant Number JPMJCR20D2, Japan, and JST PRESTO Grant Number
JPMJPR21C8, Japan.

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