When a CATMA user defines annotation classes (tags) and arranges them in a class/subclass (tag/subtag) hierarchy, the user is specifying what kinds of annotations shall exist (when it comes to annotation classes, what there is is what the user says there is). Any CATMA tag set is thus a classification scheme for annotations (since each annotation is created as an instance of some specific annotation class (tag)), and implies an ontology.

As noted above, we assume that for any class in a classification scheme there exists a characteristic property which holds for all and only the things belonging to the class, and that every such characteristic property can be represented formally by a characteristic predicate. In the case of annotations, the salient property is the one attributed by annotations of that class to passages in the text.[10]

It should be noted that in CATMA as in other annotation systems, the user is not required to identify the characteristic property of an annotation class or to formulate its characteristic predicate explicitly; both the characteristic property and the characteristic predicate are typically left implicit. For purposes of our argument, we are observing that they exist, not assuming that they have been explicitly defined.

The intension of any tag will as always be a set of properties to be attributed to text passages. It follows from the logic of the class hierarchy that the intension of a subtag will include the intension of its supertag. And the extension of any subtag will, by construction, be a subset of the extension of its supertag.

In the following discussion we will consider annotation classes as classifying both annotations and their target text passages. The extension of any annotation class thus contains both a set of annotations and the set of text passages annotated, and the intension of the class may involve both properties of text passages and properties of other things in the universe of discourse. When it is necessary to do so, we may single out the set of annotations or the set of text passages in the extension, or the different kinds of properties involved in the intension.

Because it can handle conflicting views of the world with equanimity, Quine's method of approaching ontology by identifying ontological commitments in already-held beliefs has, we think, potential interest and utility for annotators and for CATMA's system designers. For CATMA, the ontological commitments of concern are the ones made by annotators in declaring annotation classes and in annotating documents. CATMA seeks to minimize its own ontological commitments, in order to avoid imposing them on annotators.

It is of course true that annotations made by different annotators (or even by the same annotator) may conflict in various ways. It is also true that an annotator may be right or wrong in annotating (or not annotating) a text passage with a certain tag. We do not believe that this in itself is likely to lead to logical inconsistencies in an annotation ontology, since the only facts whose consistency is at issue are facts about what has actually been annotated how in some concrete sets of documents. For our purposes, we can regard those as brute facts.

The annotation scheme classifies annotations, and thus entails an ontological commitment to the existence of annotations. Each annotation attributes some property to some passage of the text. The ontology underlying annotation in CATMA thus also necessarily entails the existence of text passages.[11]

The reader may at this point ask whether the idea that an annotation attributes a property to a text passage also entails a commitment to the existence of properties as a nameable kind of thing. The answer, we believe, is that it depends on the annotation software. CATMA and other annotation systems provide interfaces which allow the user to ask, in effect, what annotations apply to a given text passage, or conversely what text passages are marked with a given tag (which is to say, what text passages fall into a given class).

We can formalize the membership of an annotation a in a class C with the predicate C(a) and the relation of a to a text passage x as annotates(a, x). Sentences of these forms will be the “affirmations made in the theory” for purposes of applying Quine's criterion for existence. Given such a formalization, the user interface actions mentioned above can be interpreted as finding particular sets: the set of all annotations for a given passage x is the set {a | annotates(a, x)} (read “the set of all annotations a such that a annotates x”), and the set of all passages of a given class C of annotations is the set {x | (∃a)(annotates(a, x) and C(x))} (read “the set of all passages x such that there exists some annotation a which annotates x and for which C(x) holds”).

When named properties are queried, the queries may become slightly more complex, but follow the same pattern. For example, if the tag set had a single Person tag, with named properties for age and sex, and subtags like Child, then one might wish to search for occurrences of Child with age greater than 16, to check the consistency of the annotations. Let us use Person(a) and Child(a) to identify all annotations using those two tags, and Person_age(a, n) to denote the relation holding between a Person or Child annotation a and the value n of its named property age. Then a search for all text passages marked as concerning a child with age greater than 16 is a search for the set {x | (∃a)(annotates(a, x) and Child(x) and (∃n)(Person_age(x, n) and n > 16))}.

The user interfaces described thus do not commit the annotation system to the existence of properties; in the formalization just sketched, there are no references to, or variables denoting, properties. Informal reference to “properties” in English prose can be taken as just a manner of speaking about particular predicates. It might be that a different annotation system could offer operations which would entail an ontological commitment to the existence of properties, but thus far we have not managed to think of any plausible operation which would require such a commitment.

The hierarchical structure of the tag set has two important practical uses. First, it allows an annotation interface to present tags for selection using menus and submenus whose structure reflects the user-defined hierarchy of the tag set. (From a strictly philosophical point of view this may appear a minor point; from the user interface point of view, it is not minor.)

Second, the supertag/subtag relation and the implicit relation of their intensions licenses simple but important inferences about the properties of annotations and text passages: every passage marked with the subtag may safely be inferred to possess the properties in the intension of the supertag, and thus to be legitimately treated as an instance of the supertag. In practice this means that it is convenient to be able to ask an annotation system to identify all instances of a tag and have the software return all annotations marked with either that tag or with any of its subtags, subsubtags, and so on to all levels of subtag. It is the fact that subtags inherit the intension and contribute to the extension of their supertags which justifies this inference and makes it meaningful to allow the user to search for all instances of female annotations and be shown instances of the subtags girl, woman, etc., or to search for all instances of adult annotations and be shown instances of man, woman, etc.[12] A clear understanding of the inferences licensed by the tag set's structure may make it easier to export annotations for processing using reasoning systems.

There may be other uses for the ontology implicit in a CATMA tag set, but for our further discussion we restrict ourselves to these two: guidance for the user interface and annotation-management tools, and logical inference about the properties of annotations and text passages.

Every annotation annotates some text passage; as noted above, from our point of view this amounts to saying that every annotation asserts the presence of some property in the text passage annotated. (For technical reasons we are excluding the possibility of meta-annotation.) It follows that every predicate representing the property associated with an annotation class must have at least one argument position for a text passage. For the moment, we limit our discussion to tags whose characteristic predicate has only that one argument (and is thus a unary predicate), which we will refer to as simple tags.

Simple tags have a straightforward representation in symbolic form: for every simple tag t there is some characteristic predicate Pt, which takes a single argument of type text-passage.[13] For example, suppose a project interested in gender and age roles marks passages in which characters of different ages and genders are mentioned, with the aim of comparing the vocabulary used for males and females, or for children and adults. The project may have tags named woman, girl, man, boy, each marking a passage in which a woman, girl, boy, or man is mentioned. The characteristic predicates of these tags might be woman(x), girl(x), man(x), boy(x), where x in each case is a variable denoting a text passage. Generic tags female, male, child, and adult might also be provided, in case a reference is specific in one way but not in the other.

If the generic tags are used as supertags and the more specific tags as subtags, the logical relation of the subtags to the supertags can be expressed formally in a very simple way: for any supertag A and subtag B, with characteristic predicates of the same name, the meaning of the subtag / supertag relation is “any annotation in class B is also in class A,” or equivalently “any text passage which exhibits property B also exhibits property A.” Formally, this can be expressed by the logical expression

(∀ x)(B(x) ⇒ A(x))

This may be read “For all x, if B(x) applies, then A(x) applies”, or “For any x, if x has property B, then x has property A.”

More concretely, if male and female are used as supertags for the age and gender tag set, the inference rules will take forms like this:

(∀ x)(girl(x) ⇒ female(x))
(∀ x)(woman(x) ⇒ female(x))
(∀ x)(boy(x) ⇒ male(x))
(∀ x)(man(x) ⇒ male(x))

Note that the following inference rules also apply, given the meanings indicated for these tags, but will be known to the system automatically only if a subtag can have two different supertags. If a tag set must form a strict hierarchy, these inferences will not be automatic.

(∀ x)(girl(x) ⇒ child(x))
(∀ x)(woman(x) ⇒ adult(x))
(∀ x)(boy(x) ⇒ child(x))
(∀ x)(man(x) ⇒ adult(x))

An annotation system might conceivably allow the user to specify inference rules like these explicitly, but that seems unlikely to make the user interface seem simple and intuitive. For that reason we are particularly interested in ways that allow the applicable inference rules to be constructed automatically from the ontology specified by the user in the course of defining the tag set.

Often, the properties we wish to discuss hold not of a single individual but of two or more individuals as a group. In symbolic logic, such properties are conventionally represented using predicates which take more than one argument. A sentence might take the form P(x, y) or P(x, y, z), instead of just P(x). See, for example, the discussion above about ways of representing the proposition that Frege was born in 1848.

As mentioned above, CATMA allows the definer of a tag set to associate a set of named properties with each tag, with suggested values for each. When creating an annotation, the annotator can supply a value for each named property, selecting one of the suggested values or supplying a different one. Thus instead of the tags woman, girl, man, and boy described in the preceding section, our imaginary tag set for age and gender roles might have a single tag character, with the named properties age (with suggested values like infant, child, adolescent, adult) and gender (with suggested values like male, female, and 3d-sex.[14] The characteristic property of character might then be formulated as “[this passage] describes a character with the indicated age and gender”, and its characteristic predicate might be written character(x, y, z), where x is a text passage, y a keyword indicating an age, and z a keyword indicating gender. The logical representations for passages describing women, girls, men, and boys might take forms like these:

character(x, adult, female)
character(x, child, female)
character(x, adult, male)
character(x, child, male)

The logical relations of the characteristic properties of different tags become a little more complex when the tag-set design patterns described in the preceding sections are used together.

Logically speaking, a single character tag suffices for the purposes described. But using it can be slightly tedious, requiring that the annotator mark a passage, select the tag, and then specify values for one or more named properties. It is perceptibly more convenient just to mark a passage and choose a tag. So for practical purposes, we might want a generic character, with named properties as described above, and also a set of more specific subtags for use in common cases: girl, woman, etc. Such a tag set can be put to good use, with appropriate support from the annotation system. Some of the desiderata are not (as far as we know) now supported by CATMA, so in the following discussion, our descriptions of things that annotation software might do are not descriptions of existing software but of software that could be constructed and which would (we think) be useful to those designing tag sets and restructuring their tag sets in the light of experience with their use on real texts.

But what kinds of support would be helpful, and how can the ontology implicit in the design of the tag set be used to allow that support?

Let us consider the case of a trope tag for marking of rhetorical tropes. An annotator might start work with just the one tag, using a named property (say, type) to identify the specific figure of speech appearing in the text, with a list of suggested values: metaphor, metonymy, synecdoche, and irony, with other values to be supplied during annotation as needed. As annotation proceeds, the annotator decides that it would be convenient to have one-click tags for metaphor, metonymy, synecdoche, and irony. The idea is that tagging a passage as a metaphor should be equivalent to tagging it as a trope with the named property type given the value “metaphor”, and similarly for the other subtags.

This can be formalized in either of two ways. If the subtags are assumed to have unary characteristic predicates, and the supertag a binary characteristic predicate, then the appropriate inference rules would be

(∀ x)(metaphor(x) ⇒ trope(x, metaphor))
(∀ x)(metonymy(x) ⇒ trope(x, metonymy))
(∀ x)(synecdoche(x) ⇒ trope(x, synecdoche))
(∀ x)(irony(x) ⇒ trope(x, irony))

In simple cases like this one, where each subtag has a name identical to a suggested value of a named property on the supertag, we can imagine a user interface that allows a user to define the supertag and then request that a subtag be generated automatically for each suggested value of the named property. The system could also search systematically for uses of the supertag with the suggested values, and re-tag them using the new subtag.

Another approach to this operation would use the same characteristic predicate for the supertag and each subtag, so that instead of the characteristic predicates metaphor(x), metonymy(x), synecdoche(x), and irony(x), the subtags would have the characteristic predicates

• trope(x, metaphor)
• trope(x, metonymy)
• trope(x, synecdoche)
• trope(x, irony)

The supertag would have the characteristic predicate

• (∃y)(trope(x, y))

In this case, no special inference rules would be needed to define the relation of the characteristic predicates of the subtags and the supertags. Instead, the named property of the supertag would be inherited by each subtag, and for each subtag it would automatically be assigned the appropriate value.[15]

If the supertag has more than one named property (like the character tag), then the user will need to specify which named properties to use for generating the subtags, and the user may well need to provide the names of the subtags. If the character tag has two named properties with exhaustive lists of possible values:

• age: one of infant, child, adolescent, adult
• gender: one of male, female, 3d-sex

then the system could automatically generate subtags for the Cartesian product of the two named properties, as well as subtags for cases where only one named property is specified: “male infant”, “female infant”, “3d-sex infant”, “infant”, “male child” (i.e. boy), “female child” (girl), “3d-sex child”, “child”, etc.

Also useful, but perhaps more challenging both from a logical point of view and for the software developer, would be analogous operations which group an existing set of tags together as subtags of a new supertag. Let us imagine that an annotator has begun work on a novel by tagging the places at which specific characters are described: in the case of Heidi, the annotator might have created tags for most of the speaking characters: Heidi, Dete, the Alpen-Ohi, Peter, and so on. The annotator may then realize that for purposes of analysis it would be helpful to treat all female characters as a class, and similarly for the males, so they may wish to create new supertags for female and male characters. In this case, the characteristic predicates constructed by the software are all likely to be unary predicates. The user might then create the appropriate named properties for the supertags and describe how the named properties and their values apply to the subtags, but otherwise the software can have no basis for constructing any n-ary characteristic predicates.

The operations described so far can all be offered in an annotation system with hierarchical annotation ontologies, at least in a limited way, but we think the system can be more useful if the hierarchical constraint is relaxed, so that existing subtags can be grouped together into multiple overlapping supertags: girl and woman being grouped into female characters, while girl and boy are grouped together into child.

Other patterns are doubtless possible for the automatic creation of subtypes from supertypes, or the grouping of types into a new supertype. We hope, however, that the simple examples we have described illustrate ways in which software can provide convenient facilities for managing and restructuring an annotation tag set in coherent and consistent ways, if the software is built to pay attention to the characteristic predicates implicit in the definitions of tags, and to the logical relations among characteristic predicates implied by the ontology of the tag set.