The representation of Q uant ML annotations in UMR - an exploration (2025)

Abstract: This paper explores the possibilities and the problems in using Unified Meaning Representations (UMRs) for representing annotations of quantification phenomena, according to the ISO standard scheme QuantML (ISO 24617-12:2025). We show that the semantic information in QuantML annotations can we expressed in UMR, provided that some powerful semantic concepts are introduced and a slightly more general approach is adopted for the representation of multiple scope relations. Conversion functions are defined that transform the XML-based representations of QuantML into UMR structures and vice versa. The consequences are discussed that can be drawn from this regarding the possible role of UMR and the semantics of UMR representations of quantification.

## introduction quantification is one of the most studied topics in semantics. its complexity gives rise to a plethora of questions, conceptual, linguistic, logical, and computational. @xcite used a higher-order intensional logic with categorial grammar to treat quantification in natural language. in contrast, abstract meaning representation (amr) and its extension, uniform meaning representation (umr) provide a first-order neo-davidsonian semantics which does not address many aspects of quantification, but which is attractive for its conceptual simplicity, especially when representing meaning in the form of a rooted graph. intuitively, the nodes and edges of such a graph are similar to the entity and link structures of quantml. for these reasons, and further motivated by the increasing popularity of amr and umr in natural language processing (see @xcite , this paper explores the possibility of representing the rich quanml annotations of quantification in the form of umrs. the organization of this paper is as follows. in section 2 we consider some of the characteristic features of quantml and umr, in particular the 3-level architecture of quantml with (a) a concrete syntax, which defines an xml-based representation format, (b) an abstract syntax which defines annotation structures in a format-independent way, using set-theoretic constructs, and (c) a semantics, which specifies semantic interpretations of the annotation structures of the abstract syntax. section 3 discusses some of the fundamental concepts in the annotation of quantification. in section 4 we examine the potential application of umr expressions in the semantic annotation of quantification. we do this in two steps. first, we compare the annotation of a variety of quantification phenomena using (a) the xml-based reference format of quantml, which we will refer to as quantml/xml, and (b) a umr-based representation format, which we will refer to as quantml/umr. this comparison provides insight into those aspects where the two forms seem little more than notational variants and those aspects for which the relation between the two is more complex. second, we investigate the possibility of converting representations in quantml to quantml/umr and vice versa. in the concluding section 5 we discuss how quanml/umr could fit into the architecture of iso semaf annotation standards and we consider the semantics of quant/umr annotations in this context. triples, and other set-theoretical constructs containing quantification-related concepts. annotation structures consist of entity structures, which contain information about a stretch of primary data, and link structures, which contain information relating two (or more) entity structures. the three levels are interrelated by encoding (ef), and interpretation functions; see figure 1 . since the semantics is defined at the level of the abstract syntax, alternative representation formats may be used that share the same abstract syntax, as indicated in figure 1 , and are thus semantically equivalent. this adds to the interoperability of the annotation schema. quantml is semantically rooted in davidsonian event semantics @xcite , @xcite ) and in the theory of generalised quantifiers (gqt, @xcite , @xcite . generalised quantifiers are not the logical counterparts of determiners, such as "every" and "some", but of nps like "more than fifty students" and three of the five men". in davidsonian semantics, verbs are viewed as denoting events and their np arguments as denoting participants in the events in certain semantic roles. combining the two approaches, a sentence with quantified participants like "more than fifty students protested" has at least two readings, depending on whether it is taken to describe a single protest event with a set of more than fifty students as agents, or a set of protest events with individual students or smaller numbers of students as agents, the total number of participants involved in the events adding up to more than 50. quantml supports the annotation of quantified participation in events by taking into account the following categories of information: the categories 1 -14 correspond to attributes of xml elements in the concrete syntax of quantml. some of these items are optional, in the sense of having a default value: polarity is by default 'positive', exhaustivity is 'negative', event scope is 'narrow', and repetiveness is 'at least once'. the attributes 145and 16 are exceptional in that they exist only in the concrete syntax; they do not correspond to anything in the abstract syntax or the semantics. they have been added purely to support searches in corpora where generic or modal quantification is marked up. for explanations and discussion of all the categories see @xcite . ## comparing and converting representations the unit of annotation in quantml is a clause, i.e. a grammatical unit describing an event (or set of events) and the participants involved. the quantml/xml annotation of the clause in example (2) is represented as follows. markables: @xmath0, @xmath1, @xmath2, @xmath3, @xmath4. inspecting the clause representations in ( 13 ) and ( 14 ) and the np representations in (11) and ( 12 ) we can observe the following correspondences , (15) a. for all entity structures foot_3 , i.e. for the xml @xmath5, <entity>, <cardinality>, <@xmath6, <relclause>, <@xmath7: foot_4 : for participation and predication link structures, the corresponding umr structure is the same, except that in this case the variable that is introduced does not have a counterpart in the xml representation. for example, the following correspondence holds because of clause (15a) and the present clause: together, the items in (15) define correspondences between np representations, as exemplified in (16) for the phrase "seven black kittens". the correspondences between parts of xml-and umr-representations suggest that it should not be too difficult to define conversion functions f @xmath8. a complication, however, is formed by a structural difference between the two. where a quantml/xml representation is a list of xml elements, describing events and participants, connected by pointers, a umr representation is a rooted nested structure with an event node (also called 'pred' node in umr) as the root and with the participation in the event as properties of the event. moreover, for a sentence with scope relations, which is almost every sentence, the proposals for scope representation discussed in section 2.2 add a scope node as the root directly 'above' the event node, by contrast, scope relations in quantml/xml are simply items in the list of xml elements, arbitrarily positioned. a conversion form xml to umr has to make the converted scope representation and position and place it immediately 'above' the converted event representation. to define the xml -umr conversion function we note hat a quantml/xml structure represents a clause. in the list of elements of such a representations three parts can be distinguished: (1) @xmath9, (2) a list @xmath10, and (3) elements describing participants and participation. we use the notation in (17) to designate such a list ( 17 for the elements in l e and l p the xml-umr conversion function is defined by the correspondences in (15). for converting the scope relations l s1 , l s2 , ...l sn forming l s it should be noted that their representation in quantml/xml depends on the fact that they occur in a clause representation with a @xmath11, whereas in umr they are the value of the 'pred' relation in a scope representation. their conversion to umr is therefore part of the conversion of the clause representation as a whole, specified in (18). the operation 3 is defined as follows. given two umr representations, the operation adds the second argument to the first argument through the relation expressed by the third argument. schematically: quantml/umr representation d d d d d d d d quantml/xml representation © e ' fx←u fu←x conversions decoding dfxq decoding abstract syntax c iqml semantic interpretation figure 2: semaf architecture with umr . (19) 3 ( (a / a, (b / b, r ) :a1 v1 :b1 w1 : ... ... :ak vk) :bn wn) = (a / a :a1 v1 : ... :ak vk :r (b / b :b1 w1 : ... :bn wn)) applied to the quantml/xml representation in (13) this conversion function produces the quantml/umr representation in ( 14 ). looking in the other direction, the correspondence relations in (15) are equally useful for converting subexpressions of umr representations to xml, due to their symmetry. for example, based on the correspondence (15a), the conversion of entity structure representations is defined in (20). the structural differences and the different treatments of scope are easier to convert from umr to xml than in the other direction. the list of scope relations in the (sls / scopelinks) list is converted to the list of their converted representations, with all the elements linked to @xmath12:pred relation in the (s / scope) representation. this is illustrated in (21). since quantml/umr representations can be converted to quantml/xml, the existence of a decoding function from annotations in the latter format have to expressions of the quantml abstract syntax shows that the quantml/umr representations have the same semantics as those of quantml/xml. to complete the reasoning about the two formats, we consider the decoding of quantml/umr representations directly by a decoding function to expressions of the quantml abstract syntax. ## conclusions: umr in the semaf architecture the inter-convertibility of the xml-based and the umr-based representations of quantml annotations means that quantml/umr fits perfectly into the three-level architecture of iso semaf annotation schemes, as visualized in figure 2 . it does involve the addition to umr of some of the fundamental concepts of quantml, notable those of participation (in events), of predication for dealing with copular verbs, and of adnominal modification, and it requires a more general treatment of scope. as noted in section 2.1, annotations made by a semaf annotation schema have a semantics, defined by an interpretation function which is applicable to the structures of the abstract syntax. in the case of quantml, the semantics combines event semantics and generalized quantifier theory with discourse representation theory. this semantics applies to the representation structures defined by a concrete syntax via 'decoding' functions that express the semantic information in these representations in the set-theoretic structures of the abstract syntax. from the inter-convertibility of quantml/xml and quantml/umr plus the existence of a decoding function for quantml/xml, defined in iso @xcite , it follows that quantml/umr representations can also been decoded in the quantml abstract syntax, and thus share the semantics of quantml/xml. umr and its predecessor amr are commonly viewed as a representation format for first-order logic. indeed, @xcite presented a first-order semantics for amr. the enrichment of amr to umr with scope links, inspired by quantml (see pustejovsky...????) and the extension to generalized quantifiers, as well as with other than individual participation, brings the expressiveness of umr to a higher level. since the semantics of the quantml abstract syntax is second-order (viz. second-order drt), needed for dealing with generalized quantifiers, it follows that quantml/umr representations also have a second-order semantic interpretation.