The compositional semantics of Q uant ML annotations (2023)

Abstract: This paper discusses some issues in the semantic annotation of quantification phenomena in general, and in particular in the markup language QuantML, which has been proposed to form part of an ISO standard annotation scheme for quantification in natural language data. QuantML annotations have been claimed to have a compositional semantic interpretation, but the formal specification of QuantML in the official ISO documentation does not provide sufficient detail to judge this. This paper aims to fill this gap.

## introduction the semantic annotation of quantification in natural language aims to enrich language data with information about the intended interpretation of the quantifications. the formulation of such annotations and their assignment to the data are challenging tasks, in view of the complexity of quantification phenomena in natural language. the many aspects of quantification, such as the distributivity, determinacy, countability, exhaustiveness, polarity and scope, make quantifications a major source of ambiguity and difficulty in computational semantics. one of the challenges that quantifications pose for semantic annotation and representation is that, although much of the information about quantification is located in noun phrases, there may also be quantification information floating around in the form of adverbials, or encoded in languagespecific morphosyntactic structure, or expressed by prosodic features (stress, pauses) ("you heard a dog barking?" "two dogs barked.") or typographical elements (use of capitals, underlining, punctuation). semantic annotation faces the challenge of picking up these various pieces of information and assembling them in a useful form. the quantml language is a proposal for such a form. another, fundamental challenge for quantification analysis concerns the choice of depth and detail, or 'granularity'. studies of quantification phenomena in natural language have both benefited and suffered from studies of quantification in logic @xcite . the benefits are in the deep understanding of formal properties of and fine-grained distinctions between various types of quantification, which have contributed greatly to the emergence of the theory of generalized quantifiers (gqt, @xcite . on the negative side, logic-based approaches tend to have weaknesses from an empirical linguistic point of view, since the fine-grained distinctions that can be expressed in formal logic tend to carry over to semantic representations of natural language expressions, while speakers and listeners are often unaware of these fine distinctions, thus creating a sort of artificial ambiguities. at this point semantic annotations may come in useful. a semantic annotation can be regarded as expressing constraints on the meaning of certain language data, without having the ambition of providing fullblown semantic representations, viz. to express 'the meaning' of the data. annotations, by contrast, may express fewer or more, weaker or stronger constraints on interpretation. still, in a context where high-precision interpretations are required, a semantic annotation scheme should allow detailed information to be captured by the annotations. the present stage of defining an iso standard annotation scheme for quantification, involving quantml is documented in iso cd 24617-12 (2023)(see @xcite . it follows the general principles for semantic annotation laid down in iso 24617-5, principles of semantic annotation @xcite (see also @xcite . one of these principles is that semantic annotations must have a well-defined semantics. in view of the challenges mentioned above, this means for quantml the re-quirement to be flexible in the level of detail of its expressions, while having a semantics for its annotation structures, regardless the level of detail. the specification of quantml in the iso document goes a long way in this direction, outlining a compositional semantics of annotation structures, but this is not fully worked out for some of its structures. the present paper aims to remedy this. the paper is organised as follows. section 2 summarises the approach taken in developing quantml. section 3 discusses the annotation of scope relations, distinguishing wider, equal, and dual scoping. the semantics of these relations is considered, and their role in combining information from pairs of quantifications. section 3 generalizes the semantic interpretation of annotations of multiple scoped quantifiers. section 4 briefly discusses the instruments available in quantml for varying the level of granularity in annotations. section 5 wraps up and closes the paper. ## iso 24617-1and quantml following the iso principles of semantic annotation @xcite , quantml has a triplelayered definition, based on a metamodel. the three layers are (a) an abstract syntax, using ntuples of concepts; (b) a reference representation format based on xml, with encoding-and decoding mappings to the abstract syntax; and (c) a semantics, in the form of a function i q which translates abstract annotation structures into drss in a compositional way. the fact that the semantics is defined for the abstract syntax makes it possible to accommodate alternative representation formats, while preserving the meaning. an example of the abstract and concrete syntax of a quantml annotation is given in (1). ## granularity in quantml annotations the preceding sections were inspired by the aim of allowing fine-grained annotation of quantification in a semantically well-defined way. as mentioned in section 1, another important aim of semantic annotation is to allow representations which are not so fine-grained, since in many use contexts it is not relevant to make very fine-grained interpretations. this is especially true of quantifications, where issues of scope, distributivity, and exhaustiveness are not in all use cases of great interest. in this section we briefly consider the instruments that are available in quantml for making annotations that are not maximally fine-grained. first, quantml annotations are modular. the abstract syntax of clause annotation structure contains a collection of entity structures and link structures when some of the components are missing, due to incomplete information, this and does not necessarily make the annotation structure uninterpretable, but allows it for example to be interpreted as an underspecified drs @xcite . second, some of the information in an annotation structure may be optional. @xcite distinguish three types of optionality, which are all present in quantml. semantic optionality is that an annotation structure may have a certain component, according to its abstract syntax definition, but is also allowed without that component. examples are the specification of the size of a reference domain and the specification of non-restrictive modifiers. annotation structures with such components have a more specific semantics. syntactic optionality is that a certain component does not need to be specified in annotation representations (using xml or some other format) but does have a default value in the encoded abstract syntax. examples are the polarity and event scope of participation link structures. finally, it may be convenient to allow certain components in concrete representations which do not encode anything in the abstract syntax, and thus have no semantic interpretation. example are the marking up of a quantification as generic and, in iso-timeml (iso 24617-1:2012) the encoding of parts of speech to distinguish verbal from nominal descriptions of events. third, some aspects of the information may be specified by more or less specific values. an example is the "unspecific" distributivity, which allows participant sets containing both individual objects and sets of individual objects. this is illustrated in plint structures of the form (8e) and(8f). ## concluding remarks this paper presents certain details of the semantic definition of quantml annotations that have so far been outlined only sketchily in the formal specification of quantml (iso cd 24617-12: 2023; see also @xcite . various forms of merge operation on discourse representation structures, relying on pattern matching techniques, have been shown to allow for a compositional interpretation of annotation structures that describe quantifications in terms of sets of events and multiple sets of participants. with the availability of the instruments mentioned in the previous section for avoiding being over-specific, quantml aims to strike a balance between allowing fine-grained and more coarsegrained, empirically useful annotations of quantification phenomena, supported in all case by a compositional semantic interpretation.