Thinking about schema mappings

[3 August 2008]

At the Digital Humanities conference in Finland in June, two papers made me think about a problem that has worried me off and on for a long time, ever since Mark Olsen at the ARTFL Project at the University of Chicago asked how he was supposed to provide searches across a large collection of documents, if all the documents were marked up differently.

Mark’s solution was simple, Procrustean, and effective: if I understood things correctly and remember aright, he translated everything into a single common vocabulary, which in the nature of things was a sort of lowest common denominator of text structure.

Stephen Ramsay and Brian Pytlik Zillig spoke about “Text analytics: a TEI format for cross-collection text analysis”, in which they described an approach similar to Mark’s in spirit, but crucially different in details. That is, like him their idea is to translate into a single common system of markup, so that the collection they are searching uses consistent ways of signaling textual features. Along the way, they will throw away information they believe to be of no interest for the kind of text analysis their tool is to support. The next day, Fotis Jannidis and Thorsten Vitt gave a paper on “Markup in Textgrid”, which also touched on the problem of providing a homogeneous interface to a heterogeneous collection of documents; if I understood them correctly, they didn’t want to throw away information, but were planning simply to store both the original and a modified (homogenized) form of the data. In the discussion period, we discussed briefly the relative merits of translating the heterogeneous material into a common format and of leaving it in its original formats.

The translation into a common format frequently involves loss of some information. For example, if not every document in the collection has been encoded in such a way as to mark all line-end hyphens according to the recommendations of the MLA’s Committee on Scholarly Editions, then it may be better to strip that information out rather than expose it and risk allowing the user to conclude that the other documents were printed originally without any line-end hyphens at all (after all, the query shows no line-end hyphens in those documents!). But that, in turn, means that you’d better be careful if you expect the work performed through the common interface to produce results which may lead to someone wanting to enrich the markup in the documents. If you’ve stripped out information from the original encoding, and now you enrich your stripped copy, later users are unlikely to thank you when they find themselves trying to re-unify the information you’ve added and the information you stripped out.

It would be nice to have a way to present heterogeneous collections through an interface that allows them to look homogeneous, without actually having to lose the details of the original markup.

It has become clear to me that this problem is closely related to problems of interest in relational databases and in RDF queries. (And probably in other areas where people worry about query languages, too, but if Topic Maps people have talked about this in my hearing, they did so without my understanding that they were also addressing this same problem.)

“Ah,” said Enrique. “They used the muffliato spell on you, did they?” “Hush,” I said.

Database people are interested in this problem in a variety of contexts. Perhaps they are performing a federated search and the common schema in terms of which the query is formulated doesn’t match the actual schemas in which the data are stored and exposed by the database management systems. Perhaps it’s not a federated query but there are other reasons we (a) want to query the data in terms of a schema that doesn’t match the ‘native’ schema, and (b) don’t want to transform the storage from the native schema into the query schema. My colleague Eric Prud’hommeaux has been working on a similar problem in the context of RDF. And of course as I say it’s been on the minds of markup people for a while; I’ve just found a paper that Nancy Ide and I wrote for the ASIS 97 conference in which we tried to stagger towards a better understanding of the problem. I have the sense that I understand the problem better now than I did then, but I could be wrong.

Two basic techniques seem to be possible, if you have a body of data in one vocabulary (let’s call it the “source vocabulary”) and would like to be able to query it using terms from a different vocabulary (the “target vocabulary”). Both assume that it’s possible to map information from the source vocabulary to the target vocabulary.

The first technique is Mark Olsen’s: you have or develop a mapping to go from the source vocabulary to the target vocabulary; you apply that mapping. You now have data in the target vocabulary, and you can query it in the usual way. Done. I believe this is what database people call “materializing the view”.

The second technique took me a while to get my head around. Again, we start from a mapping from the source vocabulary to the target vocabulary, and a query using the target vocabulary. The technique has several steps.

  1. Invert the mapping, so it maps from the target vocabulary to the source vocabulary. (Call the result “the inverse mapping”.)
  2. Apply the inverse mapping to the query, to produce a semantically equivalent query expressed in terms of the source vocabulary. (Since the query is not itself a relational database, or an RDF graph, or an XML document, there’s a certain sleight-of-hand going on here: even if you have successfully inverted the mapping, it will take some legerdemain to apply it to a query instead of to data. But just how hard or easy that is will depend a lot on the nature of the query and the nature of the mapping rules. One of the reasons for this klog post is that I want to be able to set up this context, so I can usefully think aloud about the implications for query languages and mapping rules.)
  3. Apply the source-vocabulary query to the source-vocabulary data. Simple, right? Well, no, not simple, but at least it’s a well known problem.
  4. Take the results of your query, and apply the original source-to-target mapping to them, to produce results expressed in / marked up in the target vocabulary.

Eric Prud’hommeaux may have been surprised, when he brought this topic up the other day, at the speed with which I told him that the key rule which any application of the second technique must obey is a principle I first learned in a course on language pedagogy, years ago in graduate school. (If so, he hid it well.)

The unit of translation is the utterance, not the word.

Everything else follows from this, so let me say it again. The unit of translation is the utterance, not the word. And almost every account of ‘semantic mapping’ systems I have heard in the last fifteen years goes wrong because it assumes the contrary. So let me say it a third time. The specific implications of this may vary from system to system, and need some unpacking I’m not prepared to do this afternoon, but the basic principle remains what I learned from Gertrude Mahrholz thirty years ago:

The unit of translation is the utterance, not the word.

More on this later. In the meantime, think about that.

2 thoughts on “Thinking about schema mappings

  1. Dear Michael,
    while in linguistics, the unit of translation is the utterance, I believe that it’s because linguistic texts are unstructured. With structured data, the unit of translation is defined by the schema (of whatever form). Many schemas (in my limited experience) partition the data into chunks that are independently meaningful, and therefore translatable.

    Are you saying that people creating mappings (translations) often don’t realize that the chunks are bigger, more coarse-grained, than one might think? Or is the chunk the definition of an utterance (as opposed to, let’s say, document)?

  2. Thanks for the post which created a context for our paper which I didn’t see before. On the more concrete level we discussed that problem in our paper I see two aspects which seem to be relevant:
    1) The relation between source and target schema. It could be anything you like but in the world of text retrieval for non specialists the possible degrees of variation are reduced. In Textgrid we went for the approach to use text types because we think they are the most solid ontology on texts known to users and will be the basis for most searches going beyond a full text search (this may be different for specialist searches / text retrieval as in the Monk projekt).
    2) How to execute the query. You can apply the query to a new corpus which has been converted to the target schema or you can apply the query to the original corpus which has been enriched by adding the target schema information – I think, you Michael, proposed that in our session; as the target format is a subset of some kind of the source vocabulary this is not only a question of storage, isnt it? Or you can convert the query into the source format and convert the result to the target vocabulary as you outlined above. The basic idea in Textgrid is to search in a new corpus but then show the results (after the first kwic list) in the source format.
    I didn’t understand the comparison to linguistics either: what would be the
    utterance in markup?

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