Social media are of increasing importance in current public discourse. In RANT, we aim to contribute methods and formalisms for the extraction, representation, and processing of arguments from noisy text found in discussions on social media, using a large corpus of pre-referendum Twitter messages on Brexit as a running case study. We will conduct a corpus-linguistic study to identify recurring linguistic argumentation patterns and design corresponding corpus queries to extract arguments from the corpus, following a high-precision/low-recall approach. In fact, we expect to be able to associate argumentation patterns directly with logical patterns in a dedicated formalism and accordingly parse individual arguments directly as logical formulas. The logical formalism for argument representation will feature a broad range of modalities capturing real-life modes of expression such as uncertainty, agency, preference, sentiment, vagueness, and defaults. We will cast this formalism as a family of instance logics in the generic logical framework of coalgebraic logic, which provides uniform semantic, deductive and algorithmic methods for modalities beyond the standard relational setup; in particular, reasoning support for the logics in question will be based on further development of an existing generic coalgebraic reasoner. The argument representation formalism will be complemented by a flexible framework for the representation of relationships between arguments. These will include standard relations such as Dung's attack relation or a support relation but also relations extracted from metadata such as citation, hashtags, or direct address (via mention of user names), as well as relationships that are inferred from the logical content of individual arguments. The latter may take on a non-relational nature, involving, e.g., fuzzy truth values, preference orderings, or probabilities, and will thus fruitfully be modelled in the uniform framework of coalgebra that has already appeared above as the semantic foundation of coalgebraic logic. We will develop suitable generalizations of Dung's extension semantics for argumentation frameworks, thus capturing notions such as `coherent point of view' or `pervasive opinion'; in combination with corresponding algorithmic methods, these will allow for the automated extraction of large-scale argumentative positions from the corpus.