Answer-set programming ( \(\textsf{ASP} \) ) is a declarative logic programming paradigm that provides an efficient problem-solving approach in logic-based artificial intelligence ( \(\textsf{AI} \) ). While it has proven successful, \(\textsf{ASP} \) encounters specific situations where its language falls short of accurately representing and reasoning about incomplete information. Researchers now widely agree that \(\textsf{ASP} \) requires powerful introspective reasoning with the use of epistemic modal operators; yet, despite long-lasting debates on how to extend \(\textsf{ASP} \) with such operators, they cannot reach a consensus on satisfactory semantics. Cabalar et al. argue that such research should be grounded in formal robustness. Thus, inspired by \(\textsf{ASP} \) ’s foundational properties, they introduce a structural principle called epistemic splitting and designate it as one of the compulsory criteria for epistemic \(\textsf{ASP} \) . This paper generalises their approach to a more comprehensive, meticulous, and conservative extension of \(\textsf{ASP} \) -splitting, thereby enhancing its applicability and efficiency.