Abstract
An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element d. The involution, i.e., the function \({x \mapsto x\backslash d}\), of an IRL induces a lattice anti-isomorphism, and is also an order-2 bijection of the underlying set. We examine which such bijections may be induced by the involution of an IRL.
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