Towards Cross-Linguistic Semantic Grounding using Dictionary Graph Analysis (2024)

Abstract: Previous work has explored the structure of dictionaries as directed graphs, with arcs between words when one word is used in the definition of another. We analyze the efficacy of these methodologies and explore the cross-linguistic patterns of the strongly connected components of multiple monolingual dictionaries. We find that the number of sources in the condensation graph of a directed dictionary graph is roughly stable across multiple different languages, and present future research directions.

## introduction explanatory dictionaries are an important tool for lexical semantics. however, to connect lexical meaning to real-world senses, not all meanings can be defined in terms of words; some words must be defined outside of the language in terms of sensorimotor experience. this observation is the symbol grounding problem @xcite . some theories, especially in cognitive semantics, solve this problem by considering specific words or concepts as fundamental within a language and crosslinguistically (e.g., semantic primes @xcite ). one empirical approach towards this problem is to analyze dictionary structures, modeling them as directed graphs (e.g., @xcite ). there are two major approaches for analyzing dictionary graphs. the first approach considers feedback vertex sets (fvs's) @xcite . for a directed graph d, a feedback vertex set is a set of vertices f ⊆ v (d) such that d \ f is acyclic. the minimum feedback vertex set problem consists of finding an fvs that is minimum with respect to cardinality. for semantic grounding, these sets have a convenient theoretical interpretation: if words from an fvs are removed, the dictionary becomes "grounded", i.e. there are no self-referential definitions. the second approach considers the dictionary structure through strongly connected components, or sccs @xcite . for a directed graph d, a scc is a maximal vertex set s ⊆ v (d) such that there exists a directed path in d between every pair of vertices in s. the condensation of a graph is the graph obtained by contracting each scc into a single vertex. sccs partition a directed graph into equivalence classes, and the corresponding condensation graph is acyclic. thus, the condensation graph captures the structure between groups of "equivalent" words, and the sources (i.e., vertices with no incoming arcs) represent ungrounded groups. vincent-lamarre et al. presented a taxonomy of the dictionary latent structure in this manner, with the sources in the condensation graph called the "core" foot_0 , and all other non-trivial sccs referred to as "satellites". they also analyzed the psycholinguistic correlates of the words at various levels of the latent structure, finding words in the core to be more frequent, less concrete, and learned earlier than those in the satellites. thus, the core occupies a fundamental role in the dictionary's structure. while fvs's can be more directly interpreted as grounding a dictionary (by removing selfreferential definitions), there are major downsides. the minimum fvs problem is np-hard @xcite , and the minimum sizes scale with the dictionary (vincent-lamarre et al., 2016). fvs's are not unique, so we must arbitrarily choose one for comparison. by contrast, the sccs of a digraph are unique and efficient to compute. they consider groups of self-referential words, and thereby remove arbitrary choice, facilitating cross-linguistic comparison. this study utilizes the sccs approach to identify common structure of monolingual dictionaries to lend credence to the cross-linguistic aims of cognitive semantics theories. in contrast to prior literature that focused only on english ## methods we acquired monolingual dictionaries 2 from the wiktionaries for english, french, german, mandarin, russian, and spanish using wiktextract (ylonen, 2022), based on their availability of parsed data. we limited our analyses to content words by filtering for entries with a part of speech tag of either noun, verb, adjective, or adverb, and with the python library stopwordsiso to remove function words. the definitions for all word senses for each entry were tokenized and lemmatized by stanza @xcite . the dictionaries were processed into directed graphs. each headword was treated as a vertex, and an arc was added from vertex u to vertex v if the wordform u was included in at least one definition of v. for undefined words used within a definition, an arc from the lemma form was added, and if the lemma was not present, the word was excluded. the final dictionary directed graph was preprocessed. all leaves (vertices with no outgoing arcs) were removed recursively, since they were unused in definitions and not directly relevant for the analysis. this removed all trivial sccs. we built the condensation graph of the directed dictionary graph using the built-in function from networkx @xcite , and finally extracted the sources from the condensation graph. ## results and discussion from each of the six monolingual dictionaries, we found the condensation graphs and sources within those graphs. observe that, overall, the number of sources in the condensation graphs are relatively close crosslinguistically. mandarin appears to be an outlier, with 648 sources; however, it was the smallest dictionary by far with only 25,736 words in total. without mandarin, the number of sources in 2 the dictionaries were accessed on 7/20/2024.