Attempts made by communication scholars, political and data scientists to study digital media content at a large scale through Natural Language Processing (NLP) methods have increased in the last decade, particularly to identify expressions of phenomena like populism, hate speech, or polarization. But these attempts face several methodological issues. For example, in relation to polarization, Németh (2023) argued that only a few studies have been interdisciplinary, and/or combined a qualitative approach with the application of NLP methods. Moreover, most relied on certain methods (e.g., sentiment analysis or topic modelling) and avoided others that require a deeper understanding of language articulations (e.g., dependency parsing). Semioticians have addressed similar objects of study, but most have preferred to work at a theoretical level (e.g., Monteiro Borges and Rampazzo Gambarato, 2019) or to analyze small samples in depth (e.g., Nogueira de Castro Monteiro, 2016; Hussein and Aljamili, 2020; Demuru, 2021). In this paper, I propose instead an interdisciplinary framework, and explain how the operationalization of semiotic models and concepts can guide the combined application of NLP methods to study online sociopolitical phenomena in depth at a large scale. As an example, in this paper I operationalize and computationally trace the structures suggested by the notions of competence, cognitive sanction, and axis of desire, by analyzing Facebook posts published by main right-wing candidates in the most recent Peruvian (general) and Australian (federal) elections, to reveal how the presence or absence of verbal signs and the relationships between them may reveal polarizing communication patterns.