In this paper we present an algorithm to anchor floating quantifiers in Japanese, a language in which quantificational nouns and numeral-classifier combinations can appear separated from the noun phrase they quantify. The algorithm differentiates degree and event modifiers from nouns that quantify noun phrases. It then finds a suitable anchor for such floating quantifiers. To do this, the algorithm considers the part of speech of the quantifier and the target, the semantic relation between them, the case marker of the antecedent and the meaning of the verb that governs the two constituents. The algorithm has been implemented and tested in a rule-based Japanese-to-English machine translation system, with an accuracy of 76% and a recall of 97%.
One interesting phenomenon in Japanese is the fact that quantifiers can appear in two main positions, as pre-modifier in a noun phrase (1), or 'floating' as adjuncts to the verb phrase, typically in pre-verbal position (2).1,2
| (1) | watashi-wa | 3-ko-no | kêki-wo | tabeta | ||
| I-TOP | 3-CL-ADN | cake-ACC | ate | |||
| I ate three cakes | ||||||
| (2) | watashi-wa | kêki-wo | 3-ko | tabeta | ||
| I-TOP | cake-ACC | 3-CL | ate | |||
| I ate three cakes | ||||||
Quantifier 'float' of numeral-classifier combinations is wideIy discussed in the linguistic literature.3 Much of the discussion focuses on identifying the conditions under which a quantifier can appear in the adjunct position. The explanations range from configurational (Inoue, 1983; Miyagawa, 1989) to discourse based (Downing, 1996; Alam, 1997). we shall discuss these further below. There has been almost no discussion of other floating quantifiers, such as quantificational nouns.
We call the process of identifying the noun phrase being quantified by a floating quantifier 'anchoring' the quantifier. The necessity of anchoring floatIng quantifiers for many natural language processing tasks is widely recognized (Asahioka et al., 1990; Bond et al., 1996), and is important not only for machine translation but for the interpretation of Japanese in general. However, although there are several NLP systems that incorporate some solution to the problem of floating quantifiers, to the best of our knowledge, no algorithm for anchoring floating quantifiers has been given. We propose such an algorithm in this paper. The algorithm uses information about case-marking, sentence structure, part-of-speech, noun and verb meaning. The algorithm has been implemented and tested within the Japanese-to-English machine translation system ALT-J/E (Ikehara et al., 1991).
The next section describes the phenomenon of quantifier float in more detail. We then propose our algorithm to identify and anchor floating quantifiers in Section 3. The results of implementing the algorithm in ALT-J/E are discussed in Section 4 and some remaining problems identified. The conclusion summarises the implementation of the algorithm and highlights some of its strengths.
First we will give a definition of quantifiers. Semantically, quantifiers are elements that serve to quantify, or enumerate, some target. The target can. be an entity, in which case the number of objects is quantified, or an action, in which case the number of events (i.e. iterations of the action) are quantified. The quantification can be by a cardinal number, or by a more vague expression, like several or many.
In Japanese, quantifiers (Q) are mainly realised in two ways: numeral-classifier combinations (XC) and quantificational nouns (N). Note that these nouns are often treated as adverbs, as they typically function as adjuncts that modify verbs, a function prototypically carried out by adverbs. They can however head noun phrases, and take some case-markers, so we classify them as nouns.
Numeral classiflers form a closed class, although a large one. Japanese and Korean both have two or three hundred numeral classiflers (not counting units), although typically individual speakers use far less, between 30 and 80 (Downing, 1995, 346).
Syntacticaily, numeral classifiers are a subclass of nouns. The main property distinguishing them from prototypical nouns is that they cannot stand alone. Typically they postfix to numerals, forming a quantifier phrase, although they can also combine with the quantificational prefIx sû "some" or the interrogative nani "what" :
| (3) | 2-hiki "2 animals" | (Numeral) | |||
| (4) | sû-hiki "some animals" | (Quantifier) | |||
| (5) | nan-biki "how many animals" | (Interrogative) |
Semantically, classifiers both classify and quantify the referent of the noun phrase they collocate with.
Quantificational nouns, such as takusan "much/many" , subete "all" and ichibu "some" , only quantify their targets, there is no classification involved.
Numeral classifier combinations appear in seven major patterns of use (following Asahioka et al. (1990)) as shown below (T refers to the quantified target noun phrase, m is a case-marker):
| Type | Form | XC | N |
| pre-nominal | Q-no T-m | + | + |
| appositive | TQ-m | + | - |
| floating | T-m Q Q T-m | + | + |
| partitive | T-no Q-m | + | + |
| attributive | QT-m | + | - |
| anaphoric | T-m | + | - |
| prodicative | T-wa Q-da | + | - |
Noun quantifiers cannot appear in the appositive, attributive, anaphoric and predicative complement patterns.
In the pre-nominal construction the relation between the target noun phrase and quantifier is explicit. For numeral-classifier combinations the quantification can be of the object denoted by the noun phrase itself as in (6); or of a subpart of it as in (7) (see Bond and Paik (1997) for a fuller discussion). For nouns, only the object denoted by the noun itself can be quantified.
| (6) | 3-tsû-no | tegami | ||
| 3-CL-ADN | letter | |||
| 3 letters | ||||
| (7) | 3-mai-no | tegami | ||
| 3-CL-ADN | letter | |||
| a 3 page letter | ||||
In the partitive construction the quantifier restricts a subset of a known amount: e.g., tegami-no 3-tsû "three of the letters". This is a very different construal to the pre-nominal construction. Only rational quantificational nouns can appear in the partitive construction.
The floating construction, on the other hand, has the same quantificational meaning as the pre-nominal. Two studies indicate that there are pragmatic difTerences (Downing, 1996; Kim, 1995). Pre-nominal constructions typically are used to introduce important referents, with nonexistential predicates, while floating constructions typically introduce new number information. In addition floating constructions are used when the nominal has other modifiers, and are more common in spoken text.
We will restrict the following discussion to the difference between the pre-nominal and floating uses.
There have been many attempts to describe the situations under which the floating construction is possible, almost all of which only consider numeral-classifier constructions.
The earliest generative approaches suggested that the target in the floating construction must be either subject or object. Inoue (1983) pointed out that quasi-objects, noun phrases marked with the accusative case-marker but failing other tests for objecthood, could also be targets.
Miyagawa (1989) gives a comprehensive configurational explanation, where the target and quantifier must mutually c-command each other (that is, neither the target nor the quantifier dominates the other, and the first branching node that dominates either one, dominates the other). The restriction to nominative and accusative targets is explaIned by proposing a difference in structure. Verb arguments subcategorized for in the lexicon are noun phrases, where the case-marker is a clitic and thus can be c-commanded, whereas adjuncts are headed by their markers, to form post-positional phrases which are thus not available as targets.
The c-command relation is applied to both the noun phrases themselves and traces. Quantifiers can be scrambled (moved from their base position after their target) leaving a trace if the target is an affected Theme NP, and the target and quantifier are governed by the verb that assigns this thematic role. Thus quantifiers associated with affected themes can move within the sentence. Affected themes are things that are "changed, created, converted, extinguished, consumed, destroyed or gotten-rid of" .
Miyagawa (1989, 57.) proposes a syntactic test for affectiveness: affected themes can occure in the intransitive resultative construction -te-aru.
Alam (1997) looks at the problem from a different angle, and proposes that only quantifiers which are interpreted "distributively or as a quantified event" can float, as they take wide scope beyond the NP. A quantified noun phrase will also quantify the event if the noun phrase measures-out the event, where "direct internal arguments undergoing change in the event described by the verb measure out the event" a very similar description to that of affected theme. However, Jackendoff (1996) has shown that a wide variety of arguments can measure out processes, not just subjects and objects, but also the complements of prepositional phrases. Which case-roles measure out the process can be pragmatically determined as well as lexically stipulated, so it is not a simple matter to determine which arguments are relevent.
The excellent distributional analysis of Downing (1996) shows that actual cases of floating tend to be absolutive, that is quantifiers largeIy float from intransitive subjects (67%) or direct objects of transitive verbs (24%) rather than from transitive subjects (4%) or indirect objects (1%).
On the question of why quantifiers appear outside of the noun phrases they quantify, there have been two explanations: Discourse new information floats to the pre-verb focus position (Downing, 1996; Kim, 1995), quantifiers float from noun phrases that 'measure out' an event (Alam, 1997).
We speculate that there may be a performance based reason. Hawkins (1994) has shown that many phenomena claimed to be discourse related are in fact largely due to performance. However we have not yet compiled sufficient empirical evidence to show this conclusively.
The proposed algorithm is outlined in Figure 1. In our implementation it is appplied to each of one or more candidate outputs of a Japanese dependency parser as part of the semantic ranking.
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The first step is to identify potential floating quantifiers.
Every adjunct case element headed by a noun is checked. All numeral classifier combinations are potential candidates.
An adjunct must must meet two conditions to be considered a floating quantificational nouns, one semantic and one syntactic. The semantic criterion is that one of the noun's senses must be subsumed by quanta, few/some, all-part. The syntactic criterion is that the part of speech subcategory must be one of degree or quantifier adverbial.4 We use the Goi-Taikei (Ikehara et al., 1997.) to test for the senses and Miyazaki et al. (1995) for the syntactic classification.
All noun phrases that matched a case-slot marked wlth -ga (nominative) or -0 (accusative) are accepted as potential anchors. This is the traditional criterion given for potentiai anchors. Note even if the surface marker is different, for example when the case-marker is overwritten by a focus-marker such as -wa "topic", the 'canonical' case-marker will be found by our parser.
Noun phrases marked wlth -ni (dative), have been shown to be permissible candidates, but we do not allow them. Such sentences are, however, rare outside linguistics papers. We found no such candidates in the sentences we examined, and Downing (1996, 239) found only one in ninety six examples. When we tried allowing dative noun phrases, it significantly reduced the performance of our algorithm: every dative noun phrase selected was wrong. If we could determine which noun phrases measure-out the action, then they should also be considered as candidates, but we have no way to identify them at present.
Some combinations of anchor and quantifier can be ruled out. We have identified three cases: semantically anomalous cases, sentences where the quantifier modifies the verb as a degree modifier, and sentences where the quantifier modifies the verb as a frequency modifier.
Singular noun phrases In Japanese, pronouns and names are typically marked with a collectiviser (such as -tachi) if there are multiple referents (see e.g. Martin (1988, 143-154)) . A pronoun or name not so marked characteristically has a singular interpretation. For names this can be overridden by a numeral-classifier combination (8), although it is rare, but not by an quantificational noun (9).
| (8) | Matsuo-san-ga | 3-nin | shabetta | ||
| Matsuo-HON-NOM | 3-CL | spoke | |||
| 3 Matsuos spoke | |||||
| (9) | Matsuo-san-ga | takusan | shabetta | ||
| Matsuo-HON-NOM | many | spoke | |||
| Matsuo spoke a lot | |||||
In all the texts we examined, we found no examples of names modified by floating numeral-classifier combinations. We therefore block all pronouns and names not modified by a collectiviser from serving as anchors to floating quantifiers.
In Japanese, there is not a clear division between pronouns and common nouns, particularly kin-terms such as ojisan "grandfather/old man". Pronouns can be modified in the same way as common nouns, and kin-terms are often used to refer to non kin. Pronouns modified by quantifiers need to be translated by more general terms as in (10).
| (10) | kanojo-tachi-ga | 3-nin | kita | ||
| she-COL-NOM | 3-CL | came | |||
| ? 3 she came | |||||
| The 3 girls came | |||||
Classifier semantic restrictions For numeral classifiers, the selectional restrictions of the classifier can be used to disallow certain combinations. For example, -kai "event" can only be used to modify event-nouns such as shokuji "meal" or jishin "earthquake". However, the semantics are very complicated, and there is a great deal of variation, as a classifier can select not just for the object denoted by its target but also a sub-part of it. In addition, classifiers can be used to select meanings figuratively, coercing a new interpretation of their head. Bond and Paik (1997) suggest a way of dealing with this in the generative lexical framework of Pustejovsky (1995) but it requires more information about the conceptual structure of noun phrases than is currently available.
For the time being, we use a simple table of forbidden combinations. For example pointo "point" will not be used to quantify nouns denoting agent, place or abstract noun.
Noun quantifiers can be used as degree modifiers as well as quantifying some referent. If the predicate is used to state a property of the potential anchor, then a noun quantifier will characteristically be a degree modifier.
We use the verbal semantic attributes given in the Goi-Taikei (Ikehara et al., 1997) to test for this relationship. Anchoring will be blocked either if the potential anchor is nominative and the verbal semantic attribute is one of attribute transfer, existence, attribute or result or if the anchor is accusative and the verbal semantic attribute is physical/attribute transfer.
Sentence (11) shows this constraint in action:
| (11) | kodomo-ga | sukoshi | samui | ||
| child-NOM | a little | cold | |||
| * A few children are cold | |||||
| The child is a little cold | |||||
The final case we need to consider is where the noun quantifier can quantify the event or the affected theme of the event, such as (12). In Japanese, either reading is possible when the quantifier is in pre-verbal position. Anchoring the quantifier is equivalent to choosing the theme reading.
| (12) | kare-wa | kêki-wo | takusan | tabeta | |||
| he-TOP | cake-NOM | much | ate | ||||
| He ate cake a lot | (event) | ||||||
| He ate a lot of cake | (theme) | ||||||
Examining our corpus showed the theme reading to be the default. Of course, if the event is modified elsewhere, for example by a temporal modifier, then different readings are possible. The system in which our implementation was tested lacks a system for event quantification, so we were not able to implement any constraint for this phenomenon. We therefore implemented the theme reading as our default. Note that, for stative verbs with permanent readings such as shiru "know" , there is almost no difference between the two readings (13).
| (13) | watashi-wa | ratengo-wo | sukoshi | shitte-iru | ||
| I-TOP | Latin-ACC | a little | know | |||
| I know a little Latin | ||||||
| I know Latin a little | ||||||
If there are more than two combinations, the following heuristics are used to choose which one or ones to choose.
| Prefer accusative: | |
| A combination with an accusative anchor gets two points: This is to allow for the absolutive bias. | |
| Prefer left anchor: | |
| If the anchor is to the left of the quantifier score it with one point: Quantifiers tend to float to the right of their anchors. | |
| Prefer closest: | |
| Subtract one for each intervening quantifier: Closer targets are better. | |
Finally select the highest scoring combination and eliminate any combinations that include the chosen quantifier and anchor. If there is still a combination left (e.g. there were two quantifiers and two targets) then select it as well.
These heuristics rule out crossing combinations in the rare instances of two quantifiers and two candidates.
Once the best combinations are chosen, the quantifier can be anchored to its target. We consider the best way to represent this would be by showing the semantic relation in a separate level from the syntax, in a similar way to the architecture outlined by Jackendoff (1997).
Our implementation is in a machine translation system and we simply rewrite the sentence so that the floating quantlfier becomes an prenominal modifier of its target, marked with the adnominal case-marker -no. The resulting modifier is labeled as 'anchored', to allow special processing during the transfer phase.
The algorithm was tested on a 3700 sentence machine translation test set of Japanese sentences with English translations, produced by a professional human translator. A description of the test set and its design is given in Ikehara et al. (1994).
Overall, 56 possible combinations were found and 37 anchored in 3700 sentences: Table 2. Of these, 9 were anchored that should not have been, and 1 was not anchored that should have been. The accuracy (correctly anchored/anchored) was 76% (28/37), and the recall (correctly anchored/should be anchored) was 97% (28/29).
| Floating Quantifiers: | Anchored | Not anchored | |||
| Good | Bad | Good | Bad | ||
| Nouns (N): | 12 | 2 | 7 | 0 | |
| Num-Cls (XC): | 16 | 7 | 11 | 1 | |
| Total: | 28 | 9 | 18 | 1 | |
The major source of errors was from parsing errors in the system as a whole. All of the badly anchored numeral-classifiers combinations were caused by this. In this case, the algorithm has not degraded the system performance, it would have been a bad result anyway.
There were three problems with the algorithm itself. In one case an anaphoric quantifier was mistaken as a floating quantif1er, in another the verbal semantic attribute check for degree modification gave a bad result. Finally there was one case where the default blocking for semantic anomalies blocked a good combination.
TransIation of floating quantifiersNote that anchoring a floating quantifier is only the first step toward translating it. Special handling is sometimes needed to translate the anchored quantifiers.
For example, Japanese has some universal pronouns that can stand alone as full noun phrases (14) or act as floating quantifiers (15): e.g., minna "everyone" , zen'in "all members" . When they are anchored, the information about the denotation of the head carried by the pronoun is redundant, and should not be translated. A special rule is required for this.
| (14) | minna-ga | sorou | ||
| everyone-NOM | gather | |||
| All members gather. | ||||
| (15) | membâ-ga | minna | sorou | ||
| member-NOM | everyone | gather | |||
| All the members gather. | |||||
| * Everyone's members gather. | |||||
The proposed algorithm forms a solid base for extensions in various ways.
| 1. | Combine it with a fuller system of event semantics. | ||
| 2. | Make the treatment of classifier-target semantics more detailed, so that inbuilt semantic restrictions can be used instead of a table of forbidden combinations. | ||
| 3. | Use the results of the algorithm to help choose between candidate parses and integrate it with the resolution of zero pronouns. | ||
| 4. | Test the algorithm on other languages, for example Korean. |
We have presented an algorithm to anchor floating quantiflers in Japanese. The algorithm proceeds as follows. First identify potential floating quantifiers: either numeral classifier combinations or quantificational nouns. Then identify potentiai anchors: all accusative or nominative noun phrases. Inappropriate combinations are deleted, either because of a semantic mismatch between the target and quantifler, or because the quantifier is interpreted as a degree or event modifier. Finally, possible combinations are ranked, with the accusative candidate being the best choice, then the closest and leftmost. The algorithm is robust and uses the full power of currently available detailed semantic dictionaries.
The authors thank Tim Baldwin, Yukie Kuribayashi, Kyonghee Paik and the members of the NTT Machine Translation Research Group for their discussion and comments on this paper and earlier versions. The research was carried out while Daniela Kurz visited the NTT Communication Science Laboratories. Francis Bond is currently also enrolled part time as a doctoral candidate at the University of Queensland's Center for Language Teaching & Research.