Logical pluralism is commonly described as the view that there is more than one correct logic. It has been claimed that, in order for that view to be interesting, there has to be at least a potential for rivalry between the correct logics (e.g., in Field 2009, Priest 2006, Read 2006, Russell 2008). In this talk, I explore how the relevant notions of rivalry and correctness could be combined when relying on a semantic conception of rivalry in terms of disagreement. I first give a brief intuitive characterization of the sort of rivalry in question before reviewing some standard proposals on how to capture it. I argue that none of those proposals aligns well with pluralism. More recent proposals (Shapiro 2014) to adopt the semantic framework used in the debate on context-dependence and disagreement in the philosophy of language seem to do a better job, but ultimately, it remains doubtful whether the semantics of disagreement is able to capture a notion of rivalry suitable for pluralists.