Separating Argument Structure from Logical Structure in AMR (2020)

Abstract: The AMR (Abstract Meaning Representation) formalism for representing meaning of natural language sentences puts emphasis on predicate-argument structure and was not designed to deal with scope and quantifiers. By extending AMR with indices for contexts and formulating constraints on these contexts, a formalism is derived that makes correct predictions for inferences involving negation and bound variables. The attractive core predicate-argument structure of AMR is preserved. The resulting framework is similar to the meaning representations of Discourse Representation Theory employed in the Parallel Meaning Bank.

## introduction abstract meaning representation, amr @xcite , or the penman notation it is based on @xcite , puts emphasis on argument structure. in this paper i put forward a proposal to extend amrs with a logical dimension, in order to-from a formal semantics point of view-correctly capture negation, quantification, and presuppositional phenomena. it is desirable to investigate such an extension, because (i) it would make a comparison of amr with other semantics formalisms possible (in particular discourse representation theory); (ii) it would make amr suitable for performing logical inferences; and (iii) it would be an important step in sharing resources for semantic parsing. the aim is to do this in such a way that existing amr-annotated corpora @xcite ) can be relatively easily extended with the desired extensions. this is not the first proposal of extending the penman notation to handle scope phenomena. the need to do so was recognized by other researchers @xcite @xcite . @xcite extend amr with a possibility of adding explicit scope relations. this extension, however, doesn't solve a fundamental problem that amr faces, namely viewing amrs as directed acyclic graphs and basing their interpretation on this. consider examples such as "every snake bit itself" or "all dogs want to swim". in the original amr graph notation, where quantifiers are expressed as a predicate rather than taking scope, the resulting diagrams are: the corresponding interpretations for these sentences could be paraphrased as "every snake bit every snake" and "all dogs want all dogs to swim", which are not the meanings that the sentences express. let's refer to this issue as the bound variable problem. but there is a second, perhaps an even more pressing issue, which could be dubbed the scope representation problem. amrs, in their original penman format @xcite , cannot be used directly for drawing valid inferences. let me demonstrate why this is so. using the simple conjunction elimination rule (if the conjunction "a and b" is true, then "a" is true, and "b" is true), and assuming that an amr is interpreted as a conjunction of clauses, amr will make the right predictions as long as no negation is involved (e.g., it will yield the correct inference "mary left" from "mary left yesterday"). but since, in amr, negation is represented as a predicate rather than an operator that takes scope, it will make wrong predications for negated sentences (e.g., it will allow the inference "mary left" from "mary did not leave". this is why amrs need some kind of reformulation before interpretation, and that is exactly what has been proposed in earlier work @xcite @xcite . in this paper i seek the solution at the representational level. i think the contribution of this paper is that this extension is simpler of nature than those proposed earlier @xcite . it bears similarities with named graphs for semantic representations @xcite . i argue that, if we want to fix the bound variable problem and the scope representation problem, amr requires explicit scope in their representations @xcite . i propose a method to do this by keeping the underlying predicate-argument structure, and adding a second, logical layer (section 2). in section 3, a list of examples of extended amrs demonstrate the approach. some loose ends are discussed in section 4. the idea is to extend the amr with logical structure, obtaining a scoped representation amr + with two dimensions: one level comprising predicate-argument structure (the original amr, minus polarity attributes), and one level consisting of the logical structure (information about logical operators such as negation and the scope they take). this is achieved by viewing an amr as a recursive structure, rather than interpreting it as a graph, and performing two operations on them: amrs can be seen as a recursive structure by viewing every slash within an amr as a sub-amr @xcite . if a (sub-)amr contains relations, those relations will introduce nested amrs. (a constant is also an amr, following this view.) an amr (and all its sub-amrs) will be labeled by decorating the slashes with indices (indices will be indicated by numbers enclosed in square brackets). every amr is augmented by a set of scoping constraints on the labels. this way, a sub-amr can be viewed as describing a "context". the constraints state how the contexts relate to each other. they can be declared as the same contexts (=), a negated context (¬), a conditional context (⇒), or a presuppositional context (<). colons are used to denote inclusion, i.e., l : c states that context l contains condition c. note that these labels are similar in spirit to those used in underspecification formalisms as proposed in the early 1990s @xcite @xcite . the treatment of presuppositions is inspired by semantic formalism extending discourse representation theory @xcite @xcite . ## results below i illustrate the idea with several canonical examples involving existential and universal quantification, definite descriptions, proper names, and, of course, negation. ## discussion in this section i discuss some loose ends that emerged when designing amr + : the issue of inferred labels, annotation work required to implement the approach, and the conversion to triples. ## conclusion and future work the original amr notation can be extended by a layer of logical structure that gives correct interpretation of linguistic phenomena that require scope or quantification. the resulting framework bears strong similarities with discourse representation theory as implemented in the parallel meaning bank, and it deals with the bound variable problem and the scope representation problem. so what's next? let's get an amr corpus annotated with logical structure!