Dependency and (R)MRS

Note: for current purposes, this document lacks a proper introduction, in that it assumes readers know about MRS and RMRS. The MRS and RMRS languages are successful in allowing grammar writers to construct underspecified compositional semantics for a variety of languages. They can be used with feature structure formalisms, but also in a separate semantic module with other styles of syntax. RMRS can be used with syntactic approaches that have much less lexical information than grammars which have previously been used to construct compositional representations. However, there is a major disadvantage from the perspective of using these languages for human annotation: they are verbose and difficult to read. This same disadvantage also makes them unsuitable for direct use with machine learning approaches: compositional semantic features can be extracted from (R)MRS, but the structures cannot be used directly. The verbosity also makes some types of manipulation of (R)MRS unnecessarily complex algorithmically. These properties also apply (to at least some extent) to other existing compositional semantic representations. The aim of this work is to look at whether (R)MRS (as used in the DELPH-IN grammars) can be interconverted with a representation that has more of the properties of a dependency represenatation. The main reason for looking at dependency structures is to find an encoding that minimises redundancy. A dependency structure utilises relatively simple connections between elements in an utterance, while a compositional semantic representation appears much more complex. This interconversion is also theoretically interesting, in that it provides a link between compositional semantics, constituency and dependency. It should be stressed that the intention is not that the dependency structure be thought of as an alternative form of semantics: the dependency links do not have a direct semantic interpretation.1 It is clear that an (R)MRS can be converted to some type of dependencies: Stephan Oepen developed code to do this some years ago which is incorporated in the LKB system. However, the question here is whether we can come up with an encoding which is formally equivalent so that that the dependencies can be converted back into the original (R)MRS in all cases. It is clear that it would be possible to do this for individual grammars, but this would mean the representation was subject to change as the grammar changed and that annotating with dependencies would require detailed knowledge of the grammar. What we require is that the interconversion depend on general properties which hold of a group of grammars, which can be stated formally and which will be stable as the grammars develop. We also want to be able to define a 1:1 relationship, such that we can define a deterministic procedure for converting between a (R)MRS and a corresponding DMRS. The conclusion of the work discussed here is that specific properties of the semantics in DELPH-IN grammars do allow MRS representations to be encoded in a surprisingly succinct dependency style representation, which I will refer to as DMRS. We can have some confidence that these grammar properties are theoretically reasonable, because they emerged from a style of compositional semantics which has been developed after experience with multiple grammars in a range of languages and linguistic frameworks. These were developed without any idea of a translation into dependency structure. Not all styles of semantic representation would allow this straightforward transformation: the crucial attributes of DELPH-IN (R)MRS which make it possible are a) the decision to use a relatively ‘surfacy’ style of representation b) quantifer scope underspecification c) the use of a simple algebra in composition. A fourth essential property, which has emerged from the grammars but has not been discussed previously, is the notion of ‘characteristic’ variables, made more precise below, in §2.4. This is important in that it makes it possible to define a single DMRS as the canonical one corresponding to any RMRS. This paper will proceed by taking an initial simple example of an RMRS and showing a step-by-step deterministic conversion to a dependency structure in DMRS, justifying the claim that the conversion preserves information at each