Topological approaches to locative prepositions

It is well-known that locative prepositions are used to make temporal expressions, and that they have been intensively studied in theoretical, cognitive and psycho-linguistics. However, there have been few attempts to develop a theoretical framework to deal with linguistic data on the locative prepositions (see Piñón (1997), Zwarts and Winter (1997) and Zwarts (2000) for a vector semantics to capture parallelism between aspects and a certain kind of locative prepositions). There are two purposes in this paper. One is to investigate prepositions “in,” “on,” “at” and “from/to” in English that have correlations between space and time, and show how the topological properties of the locative prepositions are preserved in temporal expressions. The other purpose is to develop a theoretical framework, or what we call a “topological approach” to natural languages, in which we use topological concepts such as spaces, paths and dimensions to analyze the linguistic data.