General frames are often used in classical modal logic. Since they are duals of modal algebras, completeness follows automatically as with algebras but the intuitiveness of Kripke frames is also retained. This paper develops basics of general frames for relevant modal logics by showing that they share many important properties with general frames for classical modal logic.
"General Frames for Relevant Modal Logics." Notre Dame J. Formal Logic 44 (2) 93 - 109, 2003. https://doi.org/10.1305/ndjfl/1082637806