  The relationship between introduction and elimination rules is often described as “harmony”, or as governed by a “principle of harmony” (see, e.g. Tennant, 1978, p. 74). This terminology is not uniform and sometimes not even fully clear. It essentially expresses what is also meant by “inversion”. Even if “harmony” is a term which suggests a symmetric relationship, it is frequently understood as expressing a conception based on introduction rules as, e.g., in Read’s (2010) “general elimination harmony” (although occasionally one includes elimination based conceptions as well). Sometimes harmony is supposed to mean that connectives are strongest or weakest in a certain sense given their introduction or their elimination rules. This idea underlies Tennant’s (1978) harmony principle, and also Popper’s and Koslow’s structural characterizations (see section  2.4).  The specific relationship between introduction and elimination rules as formulated in an inversion principle excludes alleged inferential definitions such as that of the connective tonk, which combines an introduction rule for disjunction with an elimination rule for conjunction, and which has given rise to a still ongoing debate on the format of inferential definitions (see Humberstone, 2010).