 This is the main tradition of dialogical logic and the present entry will focus on it and its recent developments. Dialogical logic is considered (especially by Lorenz) as a semantic project, and was initially developed in order to overcome the limitations of operative logic (Lorenzen 1955; see also Schroeder-Heister 2008). Dialogues are finitary games about an initial formula, which is said to be valid if, and only if, the proponent has a winning strategy for it (see  Section 2.1.2). Expanding this tradition, Shahid Rahman and collaborators have made dialogical logic a framework for expressing various logics other than the initial intuitionistic logic, as presented in   Section 2.2  (see in particular Rahman 1993, Rahman and Rückert 2001, Rahman and Keiff 2005).  