The Sequence Notation: Catching Complex Meanings in Simple Graphs (2023)

Abstract: Current symbolic semantic representations proposed to capture the semantics of human language have served well to give us insight in how meaning is expressed. But they are either too complicated for large-scale annotation tasks or lack expressive power to play a role in inference tasks. What we propose is a meaning representation system that it is interlingual, model-theoretic, and variable-free. It divides the labour involved in representing meaning along three levels: concept, roles, and contexts. As natural languages are expressed as sequences of phonemes or words, the meaning representations that we propose are likewise sequential. However, the resulting meaning representations can also be visualised as directed acyclic graphs.

## introduction there are many proposals for representing meaning of natural language expressions in a formal way. these originate from various disciplines, including formal semantics @xcite @xcite @xcite , artificial intelligence @xcite @xcite , and computational linguistics @xcite @xcite . although most of these do a tremendous job in analysing meaning, i think none of them offers a meaning representation that is the ideal candidate for large-scale annotation tasks in computational semantics requiring supervised machine learning: some of them lack expressive power, some of them are only partially interpretable, some of them are tailored to specific natural languages, and yet others are featured with a complex syntax that makes them unsuitable for human annotation tasks. what nearly all of these semantic formalisms have in common is that they all share the property of using variables ranging over (first-order or higher-order) entities. representations without variables have potential advantages and benefits when we think of human annotation efforts, machine learning approaches, and meaning visualisations techniques. hence, the question i take at heart is whether it is possible to eliminate variables from formal meaning representations without losing expressive power required to interpret linguistic expressions. the goal of this paper is to propose a meaning representation that is a healthy mixture of interlinguality, simplicity, and expressiveness. with interlinguality i mean a meaning representation that is not designed to support a single language. with simplicity i mean a kind of semantic representation that supports an intuitive way of drawing a graphical representation of the meaning that it is supposed to represent. with expressiveness i mean at least the expressive power of first-order logic (i.e., quantification, negation, and conjunction) and support for discourse phenomena such as co-reference and discourse structure. current graph-based meaning representations such as amr, abstract meaning representation @xcite lack expressive power. current logic-based meaning representations such as drs, disourse representation structure @xcite are unattractive to represent as graphs as they require substantial reification @xcite . what i propose is a formalism that combines amr with drs while removing notational redundancies such as variables and punctuation symbols. it takes the attractive and simple graph-based visualisation of amr but adds the "boxes" of drs, arriving at a formalism that includes negation and quantification as in predicate logic. the formalism accommodates two ways of represent meaning: the variable-free sequential notation, and directed acyclic graphs. the variablefree sequence notation is expected to be advantageous for human annotation efforts and language technology applications that require machine learning (e.g., applying neural networks for the tasks of semantic parsing or natural language generation). this is because it doesn't require the process of using variables nor explicit indication of scope for logical operators like negation. the graph representation is convenient for human readers and for software designed to work with graphs. ## simplifying meaning representations in this section i will present a new meaning representation system. using this formalism, annotation can be done with a simple text editor. there are no logical variables but there is still support for negation and scope. the primary encoding of meaning is done in sequence notation. but the meanings can be visualised as directed acyclic graphs. the sequence notation can be applied to various meaning representation formalisms including amr and drs. in this paper i focus on the latter. ## interpreting sequences in the previous section i showed how sequential meanings can be constructed. in this section i ex-plain how they are interpreted. appendix a illustrates how sequential meanings can be converted to discourse representation structures from drt. ## related formalisms the development of the sequence notation found inspiration from a wide spectrum of semantic representation systems, ranging from the classic semantic networks, discourse representation theory, and abstract meaning representations. in this section we will discuss how they are related: what do they have in common and how do they differ? ## conclusion the meaning represention that i proposed has much in common with amr @xcite and drs @xcite . but there are notable differences. like amr but unlike drs, sequential meanings are agnostic to any method or theory of syntax. like amr, but unlike drs, sequential meanings can be viewed as simple graphs. like drs, but unlike amr, there is an explicit way of assigning scope to logical operators. unlike amr and drs, there are no variables in sequential meanings. the quote "make everything as simple as possible, but not simpler", often attributed to albert einstein, is perhaps what summarises the sequence notation. it provides a language that i think cannot be simpler than it is, at the same time making it possible to describe complex meaning representations (including negation, disjunction, quantification, and discourse structure) with a formal interpretation. as there are only binary relations, and the binary relations can be inverted, a sequential meaning can be visualised as a directed acyclic graph, resulting in graphs that are simpler than those previously proposed for discourse representation theory @xcite . the sequence notation therefore offers a visual aid for verification of meanings. i think the sequence notation is also a convenient way of annotating text with meaning representations. the notation is simple, no logical variables are needed, meanings can be manually entered and corrected in a standard text editor. the sequence notation supports the alignment between meaning representations and corresponding linguistic realisation in an approximate manner, where at least the order of the concepts corresponds with the order as they are introduced in the text by nouns, verbs, adjectives and adverbs. yet i understand that not everyone is convinced that annotation with the sequence notation would be simpler than say amr or drs. this paper has no evidence for this claim and is solely based on personal experience. additionally, i have observed that researchers with logic background have become accustomed to the use of variables, making it considerably challenging for them to abandon the familiarity of such notation. currently the sequence meaning notation has been put in practice in the parallel meaning bank @xcite . in future work the idea is to take advantage of the sequence notation and annotate larger (multi-sentence) multi-lingual documents with meaning representations that include rhetorical structure.