Balisage Paper: A formal approach to XML semantics: implications for archive standards

0. Introduction

In contrast to syntax, which is explicitly (and machine-readably) defined for XML documents through use of a schema, XML semantics is notoriously difficult to pin down. Sperberg-McQueen, et al. 2000 takes the approach of describing semantics by defining some of the processes one goes through unconsciously when interpreting the semantics of XML: what meaning elements and attributes convey, how one makes sense of seemingly conflicting statements, the different behavior of distributed and non-distributed features, etc. Renear, et al. 2002 presents the issue of XML semantics in its historic context, identifies important aspects of semantics (class relationships, feature propagation, context and reference, etc.) that are usually only specified in accompanying prose documentation—if at all, and argues for the value of a machine-readable representation scheme for markup semantics, which is one of the research goals of the BECHAMEL Project. Piez 2002 takes a more philosophical approach to XML semantics, drawing on the work of Ferdinand de Saussure and the Structuralist movement by describing markup as a layered sign system. All of these approaches take reasonably syntactically and semantically plausible markup and/or schemas as their starting point. In contrast, for this paper we aim to work towards such a schema as an idealized end goal, by characterizing the necessary— if not sufficient— semantic constraints that differentiate a schema intended for archival use from nonsense and implausible schemas, as well as schemas that fa(i.e.,il to sufficiently take semantics into account. In addition to the goal of providing a novel approach to the perenially thorny problem of XML semantics, we are particularly concerned with the interaction between the goals of archival purposes and XML semantics.

We argue that for archival purposes, XML semantics are non-trivial - i.e., (1) that the problem of XML semantics cannot be reduced to the set of all possible use cases, (2) that XML syntax and semantics differ with regard to crucial structural properties, and (3) that semantics and syntax impose independent well-formedness constraints on schemas. We examine these properties in the context of a hypothetical long-haul archival situation in which documentation may not have been preserved – and in which the agendas underpinning the original markup may not be easy to reconstruct. In such circumstances, the interpretation of a given XML markup schema will be facilitated by an ability to explicitly delineate plausible markup schemas from non-plausible schemas independent of subject-specific knowledge.

With this in mind, we provide a formal semantic characterization of traits found in good (reasonably plausible, as contrasted with merely syntactically valid) schemas, and finally propose a set of properties that characterize such schemas in a way that incorporates both semantic and syntactic considerations. We hope that specifically considering what semantic characteristics should exclude a schema from consideration as a plausible archive standard will indirectly shed light on the nature of XML semantics more broadly. However, it is not our goal in this paper to propose an exhaustive treatment of XML semantics – instead, rather to elucidate the bare minimum necessary for a scheme to be plausible. This paper is informed by linguistic methodology in the broad sense – i.e., the proposition that a characterization of the bare minimum of “grammaticality” can yield insight of broader interest. In particular, we draw upon notions developed in the modern school of semantics that began with Montague Grammar. As such, we hope that some of the developments in the field of linguistics in the last 50 years, as reflected herein, prove as insightful a lens onto markup as the earlier Structuralist school.

1. Why semantics?

The characterization of archive-appropriate schemas necessitates separating "good" (i.e., plausibly useful) schemas from the infinitely large space of valid XML schemas. At any given point in time, practical and case-specific evaluations of the utility of a given schema should suffice for most purposes. However, long-term preservation also means planning for environments in which significant amount of case-specific detail may have been lost. Lexical semantics are particularly mutable over time; the description of "symbol" provided by TEI, documents the intended significance of a particular character or character sequence within a metrical notation, either explicitly or in terms of other symbol elements in the same metDecl TEI P4 is easier to intuitively grasp given the modern English meaning of the word than based on the 15th century usage, meaning "creed, summary, religious belief" Online Etymology Dictionary. The assumptions underlying research programs are even less stable than lexical semantics; the concern with structuralist semantics was superseded in the 1960's by the controversial and short-lived generative semantics research program which was itself eventually superseded (in the 1980s and onward) by more modern schools of semantics, beginning with Montague grammar, that have drawn on techniques of formal logic for their basis. An illustrative thought experiment here is to imagine projecting markup technologies into the past to be coextensive with literacy. What XML schemas would have been created by, for instance: a Greek dramatist, St. Augustine, an early medieval Chinese chronicler, and an alchemist? And how would these schemas differ from, say, TEI? While a single modern guideline such as TEI may be able to encode the written records of this diverse group of individuals in a way that is meaningful to the modern scholar, a TEI encoding of these texts informed by modern scholarly interests would not only fail to be interoperable with the schemas devised by the original authors, but may perhaps not even be comprehensible to them.

A rich knowledge of the specific situations (intended use, cultural context, concept of authorship/citation, etc.)  in which these hypothetical schemas were created would ameliorate the situation. However, a goal of long-term preservation standards is to allow a certain degree of interoperability without crucial context-specific knowledge. One step in doing so is to separate out the relatively small set of plausibly useful schemas from the potentially vast space of valid schemas; it is the goal of this paper to outline a way of doing so.

To illustrate this, we can consider example XML using completely ridiculous schemas and some using merely implausible schemas. Examples using completely ridiculous schemas are shown below (1-3). In each of these schemas, the permitted content type of each element is the actual object, action, or part of specified by the name of the element (i.e. <branch /> can only contain such a protrusion from a tree, <simplify /> can only contain the act of simplification, etc.)

Some structurally similar schemas are intuitively less ridiculous, although also implausible. Examples of XML using implausible schemas are given below (4-7).

How, then, to distinguish between the ridiculous, the implausible, and the plausible?

An immediate and intuitive objection to these schemas might be that they can be ruled out on the grounds that no one would possibly be interested in them. However, that explanation, which can be termed the "practical usability explanation" is not fully adequate. First, it is not necessarily clear that this approach would capture the difference between the ridiculous and the merely implausible. On a certain level, the English conjunctions schema could be thought to be more plausible than the "broken clock is right twice a day" incorrect word-length schema, insofar as it is much easier to imagine why someone would be interested in conjunctions than in looking at the result of multiplying word-length figures by the sine function. However, the English conjunctions schema is clearly bad in a way that the "broken clock is right twice a day" incorrect word-length schema isn't. Intuitively speaking, we might say that conjunctions are a reasonable area of interest, but given an interest in conjunctions, the English conjunctions schema is unlikely to be your choice. On the other hand, being interested in multiplying word-length figures by the sine function is bizarrely implausible, but if for some reason one wanted to do that, the "broken clock is right twice a day" incorrect word-length schema would work.

The "practical usability explanation" is especially problematic in the context of archival preservation. Part of the reason why long-term archival preservation of XML is a non-trivial task is precisely the fact that it is not always obvious what future generations of researchers will find interesting or useful. Furthermore, the establishment of practical usability will always to a certain extent be in the eye of the beholder. Schemas like our conspiracy-theorist schema could be of potential interest - Dan Brown, for instance, could testify to the wide public appeal of conspiracy theories. More seriously, debates about intuitive assessments of practical utility are unlikely to be a fundamentally productive line of discussion.

Another possible objection is that by definition XML markup is performed on text. This renders the tree-list schema and the command-list schema impossible insofar as it is a feature of the real world that tree parts and actions are not composed of combinations of characters. While this is a reasonable objection, the degree to which these assertions are based on potentially contestible real-world knowledge is problematic. It may be difficult to imagine a situation in which a sane person would assert that trees are composed out of characters in an ontologically real sense, but one can more easily imagine a lively argument about whether actions can be expressed with words in an ontologically real sense (e.g. performatives). Regardless, this line of reasoning is only applicable with difficulty in a hypothetical long-haul preserval scenario – assumptions about real-world phenomena have been known to change over time.

What criteria, then, can we use to distinguish ridiculous, implausible, and plausible schemas without reference to practical utility or related questions? Syntax could help; an intuitive observation about schemas (1) - (7) is that they are structurally flat, an observation which leads to the suggestion that more elaborate syntactic structure may be characteristic of plausible schemas. While this may be the case, it is also the case that equally absurd examples could be constructed to an arbitrary degree of syntactic nestedness, and not all flat schemas are absurd (i.e. Dublin Core). This illustrates that syntactic considerations are not sufficient to the task at hand. The rest of this paper develops a proposal that employs semantics to characterize plausible schemas, as opposed to syntactically valid but ridiculous or implausible schemas.

2. Syntax-Semantics Mismatches in XML

A prerequisite to any discussion of XML syntax versus XML semantics is to determine whether or not XML syntax and XML semantics are on some level equivalent. If a generalization about XML semantics could be restated making reference only to XML syntax, this would render any mention of semantics irrelevant. In this section, it is shown that there are at least two senses in which syntax and semantics are crucially distinct in XML. (A note on representation; in the field of semantics, angled brackets are are used to refer to words, while square brackets refer to what the words mean, or their denotation. Therefore, in this context, <cat> refers to an element that could be employed in a schema, while [[cat]] refers to the furry animal, and <cat> refers to an XML representation. 

First, XML syntax is strictly hierarchical, but XML semantics does not have to be. An example where both syntax and semantics are hierarchal can be seen in paragraph structure: <sentence> ∊ <paragraph> (in XML, <paragraph><sentence /><paragraph>) and [[sentence]] ⊂ [[paragraph]] (a sentence is a subset of a paragraph). However, when elements refer to properties that are not inherently hierarchical, this is not the case. For instance, <damage> ∊ <sentence> but [[damage]] ⊄ [[sentence]] - i.e., the element <damage> may be the parent element for <sentence>, but it does not make sense to say that the concept of damage is a subset of the concept of sentence. This can be formalized as follows: if the subset relationship holds between the denotations of two or more elements (like [[sentence]] and [[paragraph]]), let these elements be called semantically hierarchical. If not (like [[damage]] and [[sentence]]), then let these elements be called semantically non-hierarchical. The semantic hierarchy can be captured by arranging semantically hierarchical elements on the semantic levels s, s(1), s(2), ..., s(k) for k levels of specificity (proceeding from general to specific) - i.e., the semantic hierarchy consists of semantically hierarchical elements, arranged accordingly.

As an aside, it can be noted that proposals have been made for XML syntax to be non-strictly hierarchical in order to accommodate different kinds of structures in a document Renear, et al. 1993, which stands in contrast to earlier conceptions of a document as containing a single logical hierarchy of content objects DeRose, et al. 1990. Non-hierarchical syntax involves the use of different (concurrent) structures that may overlap with one another but share the same content Chatti, et al 2007.  Syntactic non-hierarchicality applies only to interactions between different syntactic levels of the schema (although, in extreme cases, such as the Dublin Core, there may only be one level of syntax at all), and does not obviate hierarchicality in the semantics.

Syntax and semantics also impose independent constraints on the well-formedness of schemas (where well-formedness is understood as the property that characterizes plausible schemas). The independence of syntactic and semantic constraints are illustrated below; again, here the element <every> can only contain the concept of every-ness:

These considerations demonstrate that XML syntax and semantics must be analyzed as separate domains. The restrictions that hold on valid XML syntax have been well documented W3C 2008, whereas the restrictions that must hold on the semantics of plausible schemas are less well described.

3. Formal Semantics of XML

4. Some Very Basic Features of Archive Standards

In this section, we summarize the above points and add some other criteria that must be met by plausible archive standards.

5. Conclusion

Starting our exploration of XML semantics from the perspective of all syntactically valid schemas has allowed us to formalize some semantic traits shared by mostly widely-used schemas that are easy to overlook, but of great significance when assessing how useful a schema might be for archival purposes - and reverse-engineering the interpretation of schemas that have been used for archival purposes, but for which adequate documentation is lacking. This may also have implications for ongoing work towards machine-interpretation of XML semantics. If an XML document uses a schema that conforms to our proposed archive standards, stronger statements can be made about the relationship between the elements in that document. The fact that the syntactic hierarchy of elements is compatible with a real-world semantic hierarchy, in combination with the other generalizations that we have made about archive-appropriate XML semantics, facilitates the development of automatizable processes of analysis, and enables developers to bring to bear existing tools used for classifying the real world.