Taxonomy of Problems in Lexical Semantics (2023)

Abstract: Semantic tasks are rarely formally defined, and the exact relationship between them is an open question. We introduce a taxonomy that elucidates the connection between several problems in lexical semantics, including monolingual and cross-lingual variants. Our theoretical framework is based on the hypothesis of the equivalence of concept and meaning distinctions. Using algorithmic problem reductions, we demonstrate that all problems in the taxonomy can be reduced to word sense disambiguation (WSD), and that WSD itself can be reduced to some problems, making them theoretically equivalent. In addition, we carry out experiments that strongly support the soundness of the concept-meaning hypothesis, and the correctness of our reductions.

## introduction this paper proposes a taxonomy of several problems in lexical semantics, consisting of a clear definition of each task, and a theory-driven analysis establishing the relationships between them (figure 1 ). the taxonomy includes word sense disambiguation (wsd), word-in-context (wic), lexical substitution (lexsub), and word synonymy (syn). we consider their monolingual, cross-lingual, and multilingual variants. with the exception of wsd, they are all defined as binary decision problems. our theoretical problem formulations correspond to well-studied semantic tasks. in practice, these tasks are rarely precisely defined, and instead depend on annotated datasets. for example, the definitions of lexical substitution differ between papers, and involve imprecise terms, such as "the overall meaning of the context" or "suitable substitute." the exact relationships between these tasks have not been rigorously demonstrated. altogether, the recent literature suggests that a more detailed taxonomy is very much needed. we start by formally defining the problems in terms of concepts and contexts, and proceed to de-termine their relative hardness by specifying reduction algorithms which produce a solution for one problem by applying an algorithm for another. in particular, we demonstrate that all problems in the taxonomy can be reduced to wsd, which confirms the principal role of this problem in lexical semantics. furthermore, we show by mutual reductions that wsd and multilingual variants of wic and lexsub are theoretically equivalent. finally, we shed light on how they relate to lexical translation and wordnets. the soundness of the problems in the taxonomy hinges on the consistency of judgments of sameness of word meaning. @xcite demonstrate the theoretical equivalence of the monolingual wic and wsd via mutual reduction. we posit the following generalization of their sense-meaning hypothesis to multilingual concepts: different word instances have the same meaning if and only if they express the same concept. this empirically falsifiable proposition, which we refer to as the concept-meaning hypothesis, allows us to incorporate multilingual tasks, including lexical synonymy and substitution, into our theoretical framework. in addition to showing that our theoretical propositions follow directly from our definitions and assumptions, we perform a series of experiments for the purpose of testing their empirical applicability and soundness. in particular, we test three problem reductions on standard benchmark datasets using independently developed systems based on pre-trained language models. manual error analysis reveals no counter-examples to our conceptmeaning hypothesis. our main contribution is a novel taxonomy of formally-defined problems, which establishes the reducibility or equivalence relations between the principal tasks in lexical semantics. in addition, we carry out a series of experiments that support the correctness of our theoretical findings. ## theoretical formalization in this section, we formally define the problems in our proposed taxonomy, and discuss the relationship between these theoretical problems and the computational tasks addressed in prior work. ## problem reductions given an algorithm for a problem q, a p-to-q reduction solves an instance of a problem p by combining the solutions of one or more instances of q. the reducibility of p to q is denoted @xmath0. mutual reductions of two problems to one another, i.e. @xmath1, demonstrate their equivalence. in this section, we present several problem reductions, which constitute the main contribution of this paper. the reductions are shown in figure 1 by the directed arrows from p to q. the black arrows denote the special cases, which immediately reduce to the more general problems. taken together, the reductions establish the equivalence of six problems: wsd, tsv, wic, monowic, multiwic, and multilexsub. a method which solves any of these problems can be used to construct methods which solve the other problems by applying a sequence of reductions. as well, a method for one of those six problems can be used to solve any of the other problems in figure 1 , again via reductions. ## relationship to synsets a wordnet is a theoretical construct which is composed of synonym sets, or synsets, such that each synset corresponds to a unique concept, and each sense of a given word corresponds to a different synset. actual wordnets, such as princeton word-net @xcite , are considered to be imperfect implementations of the theoretical construct. we define the following monolexical problem, which decides whether a given word can express a given concept: sense(w, s) := "the word w expresses the concept s in some context" an algorithm for the sense problem could be used to decide whether a given word belongs to the synset that corresponds to a given concept. ## empirical validation in this section, we implement and test three principal reductions: multiwic to wic, multiwic to wsd, and multilexsub to wsd. for each reduction, we reiterate its theoretical basis, describe our implementation, and discuss the results. we emphasize that the goal of our experiments is not challenging the state of the art, but rather empirically testing the reductions, and, by extension, the hypothesis they are based on. since the resources used for the implementations are necessarily imperfect, and the systems are each designed and optimized for a different target task, the reductions are expected to produce much less accurate predictions on the existing benchmark datasets compared to state-of-the-art methods. our primary interest is in identifying any possible counter-examples to our concept-meaning hypothesis. however, it must be noted that the presence of a small number of such exceptions in the existing datasets does not invalidate the theory. on the other hand, the scarcity of counter-examples should not be interpreted as a proof, but rather as supporting evidence for the correctness of our theoretical claims. ## conclusion starting from basic assumptions about the expression of concepts by words in context, we have developed consistent formulations of thirteen different problems in lexical semantics. we have shown that a "wordnet-complete" subset of these tasks can each be used to solve any of the others via reduction. these problems can be used to construct, correct, or expand multilingual synonym sets, the building blocks of important linguistic resources such as wordnet and babelnet. we believe that this work will lead to a greater understanding of lexical semantics and its underlying linguistic phenomena, as well as new applications and better interpretation of empirical results. based on our theory, we intend to develop methods for constructing fully explainable and interpretable linguistic resources.