rains an error case frame to have at most one obligatory preposition. Certain verbs sometimes have more than one obligatory preposition as in range from A to B. However, the large majority of verbs satisfy rule (b). Rule (c) states that prepositions appearing left of the verb in the input sentence are optional preposition cases as in In the morning, he went shopping. Rule (c) is based on the assumption that obligatory cases are tied to the verb more strongly than optional cases. In other words, obligatory cases cannot easily change their position. Conversely, optional cases have more freedom of their position, which enables them to appear left of a verb. Admittedly, obligatory prepositions can appear left of a verb as in To school, he went in certain circumstances such as in poetry. However, this usage is not so frequent in corpora normally used as training data such as newspaper articles. Rule (d), together with rule (b), states that if more than one preposition appears right of the verb, the one nearest to the verb is obligatory and the rest are optional. Rule (d) is based on the same reasoning as in rule (c).
Optional preposition cases are sometimes determined naturally by comparing two case frames. In this case, one of them must consist of only the object(s) as its preposition case(s) as in "[go Subj:{PERSON} Prep dobj:{shopping} ]." Then, the other case frame must consist of the same verb, the same basic cases, and the same object(s). The only difference between them is preposition cases (except the object (s) (4) Grouping case frames: Similar case frames in the native case frames are grouped into one, which will play an important role in (7) Enriching error case frames. Case frames comprising similar cases tend to denote similar usage of a verb. Considering this, case frames are merged into one if they consist of the same verb, the same basic cases, and the same case tags of the obligatory preposition cases. The grouping procedure is illustrated in Fig. 4. When preposition cases are obligatory in one case frame and optional in the other, the discrepancy is resolved by setting the preposition case to optional in the merged case frame. Note that this grouping procedure is not applied to the learner case frames so that erroneous usages in the learner case frames do not propagate to other (correct) learner case frames.
(5) Selecting candidate error case frames: Candidates for error case frames are selected from the learner case frames. If a learner case frame does not match, ignoring optional preposition cases, any native case frame, it is selected as a candidate for an error case frame on the assumption that case frames corresponding to erroneous usages do not appear in the native corpus.
Alternatively, an error-annotated learner corpus can be used to select error case frames; simply extracting case frames of which preposition is marked as an error gives error case frames. In this case 3, procedure (6) may be omitted and procedure (7) is directly applied after procedure (5).
(6) Determining correct prepositions: Now, correct prepositions for the candidate error case frames are explored. Each case tag of the preposition cases in a candidate is replaced, one at a time, with one of the other target prepositions. This replacement can be interpreted as error correction. Take as an example the following candidate error case frame: [go Subj:{PERSON} Prep dobj:{shopping} Prep to:{market} ]. Replacing the case tag "Prep to" with "Prep at" corresponds to correct expressions such as John often goes shopping at the market. Note that replacing a direct object with one of the prepositions corresponds to correcting an omission error as in "Prep dobj" with "Prep to" in "[go Subj:{PERSON} Prep dobj:{market} ]". Similarly, replacing a preposition with an object corresponds to correcting an extra-preposition error (e.g., "Prep to" with "Prep dobj" in "[go Subj:{PERSON} Prep to:{shopping} ])".
To examine whether each correction is valid or not, the native case frames are again used; if the replaced case frame matches one of the native case frames, the correction is determined to be valid. Here, we define the match as the two case frames consisting of the same verb, the same basic cases, the same obligatory preposition cases, and the same preposition case to which the correction is applied (if it is an optional one). If the condition is satisfied, the information on the error and correction is added to the candidate error case frame. If a valid correction is found, the candidate is determined to be a valid error case frame. In total, their validity is double-checked, once in (5) and once in (6) Figure 4: Example of grouping case frames.
native case frames.
(7) Enriching error case frames: The generated error cases are limited in error coverage because the procedures so far solely rely on preposition errors appearing in the learner corpus. In other words, it is impossible to generate error case frames corresponding to preposition errors which do not appear in the learner corpus. To overcome this limitation, the generated error case frames are enriched using the native case frames. For each error case frame, we already know the corresponding native (thus, correct) case frame, which is obtained in (6). The corresponding native case frame is normally much richer in preposition cases because of the optional cases and grouping given by procedures (3) and (4), as shown at the top of Fig. 5. These additional cases are useful to enrich error case frames.
For the preposition case which is determined to be erroneous, its correct preposition is found in the error case frame (e.g., "→ Prep at" at the top-left of Fig. 5). Also, its correct preposition case is found in the corresponding native case frame (e.g., "Prep at:{market,store}" at the top-right). Replacing the case element of the erroneous case by one of the case elements of the correct preposition case gives a new candidate for an error case frame (e.g., replacing market of "*  corpus. Therefore, it should be discarded. Only if a match is not found, is the case element added to the erroneous preposition case in the original error case frame. This process is illustrated in the box denoted as Verification in Fig. 5. For the other preposition cases which are not erroneous, the enriching procedure is much simpler. They are simply added to the error case frame as shown in Fig. 5. One thing we should take care of is that there might be a discrepancy in obligatory/optional between the cases of the error case frame and the native case frame. This discrepancy is solved by setting the preposition case in the error case frame to optional. The resulting expanded error case frame after procedure (7) is shown at the bottom of Fig. 5 where the enriched cases are shown in red.
(8) Manually Editing Error Case Frames: The most important editing is the addition of feedback messages. A human annotator interprets the generated error case frames and adds explanatory notes to them. Although this basically requires manual editing, part of feedback messages can be automatically created to facilitate the procedure. For example, example sentences corresponding to an error case frame can be automatically added to it, whether correct or error examples, because the original sentences from which the (error) case frames extracted are available in the native and learner corpora. Besides, setting a variable to the feedback message allows it to be adaptable to correction results as shown in Fig. 6. In Fig. 6, X Prep to is a variable. It is replaced with one of the case elements of "Prep to:" depending on correction results. Also, it will be beneficial to link similar error case frames each other, which allows the user to obtain additional information. To mean traveling to a place in order to take part in an activity, go takes at, in, or on depending on the activity. For example, the activity shopping takes place at a ܺ ୮୰ୣ୮_୲୭ (not shopping to a ܺ ୮୰ୣ୮_୲୭ ), and thus go shopping at ܽ ܺ ୮୰ୣ୮_୲୭. cf. We went sightseeing in Baltimore.." One can retrieve similar error case frames from the generated error case frames where the similarity between two error case frames are defined by the overlap in the verb, the basic cases, and the case tags of the preposition cases.
The generated error case frames may be further edited to enrich them. As we can see in Fig. 5, the generated error case frames are easy to interpret. This property enables us to manually edit them to enrich their preposition cases. For example, one might add a case element such as supermarket to the preposition case "Prep to:{market,store}" in the example error case frame. Conversely, one might discard unnecessary case elements, cases, or even error case frames.

Correcting Preposition Errors
Preposition errors are corrected by applying the generated error case frames to the target text. Case frames are first extracted from the target text by the same procedures (2) and (3) in Sect. 3. Then, each extracted case frame is examined if it matches one of the error case frames. If a match is found, the preposition is detected as an error and the correct preposition is suggested with the feedback message according to the matched error case frame