Causal inference of diachronic semantic maps from cross-linguistic synchronic polysemy data

Semantic maps are used in lexical typology to summarize cross-linguistic implicational universals of co-expression between meanings in a domain. They are defined as networks which, using as few links as possible, connect the meanings so that every isolectic set (i.e., set of meanings that can be expressed by the same word in some language) forms a connected component. Due to the close connection between synchronic polysemies and semantic change, semantic maps are often interpreted diachronically as encoding potential pathways of semantic extension. While semantic maps are traditionally generated by hand, there have been attempts to automate this complex and non-deterministic process. I explore the problem from a new algorithmic angle by casting it in the framework of causal discovery, a field which explores the possibility of automatically inferring causal structures from observational data. I show that a standard causal inference algorithm can be used to reduce cross-linguistic polysemy data into minimal network structures which explain the observed polysemies. If the algorithm makes its link deletion decisions on the basis of the connected component criterion, the skeleton of the resulting causal structure is a synchronic semantic map. The arrows which are added to some links in the second stage can be interpreted as expressing the main tendencies of semantic extension. Much of the existing literature on semantic maps implicitly assumes that the data from the languages under analysis is correct and complete, whereas in reality, semantic map research is riddled by data quality and sparseness problems. To quantify the uncertainty inherent in the inferred diachronic semantic maps, I rely on bootstrapping on the language level to model the uncertainty caused by the given language sample, as well as on random link processing orders to explore the space of possible semantic maps for a given input. The maps inferred from the samples are then summarized into a consensus network where every link and arrow receives a confidence value. In experiments on cross-linguistic polysemy data of varying shapes, the resulting confidence values are found to mostly agree with previously published results, though challenges in directionality inference remain.