A Top-down Graph-based Tool for Modeling Classical Semantic Maps: A Case Study of Supplementary Adverbs (2025)

Abstract: Semantic map models (SMMs) construct a network-like conceptual space from cross-linguistic instances or forms, based on the connectivity hypothesis. This approach has been widely used to represent similarity and entailment relationships in cross-linguistic concept comparisons. However, most SMMs are manually built by human experts using bottom-up procedures, which are often labor-intensive and time-consuming. In this paper, we propose a novel graph-based algorithm that automatically generates conceptual spaces and SMMs in a top-down manner. The algorithm begins by creating a dense graph, which is subsequently pruned into minimal spanning trees, selected according to metrics we propose. These evaluation metrics include both intrinsic and extrinsic measures, considering factors such as network structure and the trade-off between precision and coverage. A case study on cross-linguistic supplementary adverbs demonstrates the effectiveness and efficiency of our model compared to human annotations and other automated methods. The tool is available at https://github.com/RyanLiut/SemanticMapModel.

## introduction a linguistic form-such as a morpheme, word, or construction-can map to multiple related meanings or functions 1 , which, in turn, correspond to different cross-linguistic forms. to analyze this multifunctionality, linguists employ semantic map models (smms) @xcite . smms construct a network, known as conceptual space, where nodes represent distinct yet related functions, and edges reflect the semantic similarity between these functions. this structure adheres to the connectivity hypothesis @xcite , which asserts that functions shared by a single form should map onto a connected foot_0 region in the conceptual space, thus preserving the limits of linguistic variation @xcite . an example illustrating typical dative functions and two forms is shown in figure 1 . constructing the conceptual space typically involves three steps. first, the semantic domain and the corresponding cross-linguistic forms are identified. second, linguists analyze a form-function table, determining whether a given form can express a specific function based on a multilingual corpus. third, edges are added and adjusted by either manual annotation or automated procedures, following bottom-up or top-down approaches guided by the connectivity hypothesis. this ensures that each subgraph-representing the multiple functions of a form (i.e., the rows in the form-function table)-remains connected. typically, this process incrementally builds the graph, edge by edge, as new instances are encountered, reflecting a bottomup approach. in contrast, our method introduces a top-down algorithm to improve efficiency. these steps are illustrated in figure 2 . however, this construction process has several limitations. first, manually adjusting the graph is both time-consuming and labor-intensive, especially when handling large datasets with a large number of languages and forms. second, although domain: supplement adv. also too again 还 又 auch noch また なお multilingual corpus i want to see this movie again. 人死了还会活过来吗？ bitte sag es noch einmal. ... su re again auch ✗ cd ✗ ... ... ✘ bottom-up top-down graph construction form-function table some semi-automated methods have been proposed to assist @xcite , they still adhere to a bottomup approach, requiring substantial manual effort to determine which edges to retain or add. third, human judgment introduces an element of subjectivity, particularly when deciding between two equally plausible connections. to address these challenges, we propose a novel graph-based algorithm for constructing the conceptual space in a top-down manner. the algorithm begins by creating a dense graph, where the cooccurrence of functions (nodes) in the same form (colexification) serves as the weights for their corresponding edges. we then prune this graph by extracting maximum spanning trees, sorted in descending order by the total weight of their edges. the optimal trees are selected based on automated metrics that include coverage of linguistic instances and network topology. this process is considered top-down because it starts with a dense but suboptimal conceptual space and is subsequently pruned into a tree constrained by our proposed hypothesis. therefore, it provides a global solution by considering all possible edges in the graph, rather than employing a bottom-up strategy that begins from a localized region formed by individual forms. a case study on supplementary adverbs demonstrates the model's competitive performance and efficiency compared to human-generated maps and other automated methods. the key contributions of this paper are as follows: supplementary adverbs supplementary adverbs are universal across multiple languages, serving to modify the meaning of verbs, adjectives, or other adverbs in a sentence and thereby providing additional contextual information. these adverbs play a crucial role in communication by indicating time, degree, manner, or continuity. researchers have conducted extensive studies on this subject, emphasizing their multifunctionality. given this high degree of multifunctionality, the work in @xcite distinguishes different functions in terms of semantic features, such as bounded, sequenced, etc. linguists focus on words in their respective languages, while still adopting a crosslingual perspective. for instance, the english adverb still is often used to indicate the continuity or persistence of an action over time @xcite . in german, noch can denote an additional action or state, while schon often implies that something has occurred earlier than expected @xcite . in chinese, the adverb 还 is used to express the continuation or inclusion of an action, whereas 有 can indicate an additional aspect of an action @xcite . some research also illustrates the evolution of these related words in a diachronic @xcite or synchronic @xcite context. in this paper, we selected supplementary adverbs as a case study for two main reasons. first, they have been extensively studied, with significant consensus in the field. second, the data scale encompassing a wide range of languages, forms, and functions is substantial, making it a particularly suitable and challenging scenario for constructing semantic maps. ## preliminary in this section, we first present some notations, then introduce the conceptual space and the semantic map. ## approach in this section, we first introduce our top-down graph-based algorithm for semantic map models (smms). following this, we design both intrinsic and extrinsic metrics. ## case study in this section, we present a case study that utilizes semantic map models (smms) to analyze adverbs related to "supplement" @xcite @xcite . the author collected 28 forms (function words) across nine languages that exhibit the "supplement" function along with 17 other related functions 7 . based on whether a form in a corpus corresponds to a given function, the author constructed the form-function table m , as shown in ## conclusion in this paper, we propose a graph-based algorithm to generate a conceptual space and semantic map in a top-down manner. this approach is realized by instantiating the conventional connectivity hypothesis into a greedy maximum spanning tree, where the weights are determined by the number of co-occurrences. to select the optimal candidate, we introduce a novel metric-diversity of degrees-based on graph topology, in addition to classical metrics such as precision, recall, and accuracy against ground truth. through a case study on supplementary adverbs, we demonstrate the effectiveness and efficiency of our approach. our visualization tool provides linguists with a valuable reference that can be manually refined further, while offering the computational community a graph-based framework for cross-linguistic semantics. this framework can be integrated with models like graph neural networks @xcite , or approaches like conceptual space modeling @xcite .