 Given the insight that not only cyclic structures of reference can lead to paradox, but also certain types of non-wellfounded structures, it becomes interesting to study further these structures of reference and their potential in characterising the necessary and sufficient conditions for paradoxicality. This line of work was initiated by Gaifman (1988, 1992, 2000), and later pursued by Cook (2004), Walicki (2009) and others.