Corrigendum: Residuation in Commutative Ordered Monoids with Minimal Zero

The assertional logic S(BCIA) of the quasivariety of BCI-algebras (in Iseki's sense) is axiomatized, relative to pure implicational logic BCI, by the rule x, y, x → y (G) (see [1]). Alternatively, the role of (G) can be played by x x → (y → y) (1) (see [2]). The formula (x → x) → (y → y) (2) is a theorem of S(BCIA). In [2, Proposition 22] we claimed erroneously that, relative to BCI, the axiom (2) is equivalent to (G) (i.e. to (1)), and we concluded that S(BCIA) is an axiomatic extension of BCI. This conclusion is also false. To correct this we verify here