A Mathematical Model of the Cognitive Semantics of the English Preposition ON

This study aims to present a mathematical linguistic analysis in establishing the relations between TRs, LMs, potential senses, and actual senses by using the case of the preposition on found in academic texts under the framework of Trajector (TR) and Landmark (LM) configurations. Data were corpora taken from 10 bachelor’s theses written by Indonesian students. To sort the data, Ant Conc 3.4.1.0 was used to parse clauses or sentences based on the TR-LM configurations. Based on the TR-LM configurations, a mathematical model was developed to discover how these variables are quantitatively related to the number of potential senses produced by using a geometric representation of TR and LM. This study indicates that the relation between TRs and LMs, on the one hand, and the sum of potential senses, on the other, follows the integral function of , which means that the total number of potential senses of Ps equals the integral of TR with respect to LM. Meanwhile, the total number of actual senses, ∑As can be obtained by the integral function of , which equals TR.LM + C where C is -Ls representing the constant of the number of lost senses. This mathematical modeling confirms that TR-LM configurations may be used to generate senses which prove the polysemous nature of prepositions.