Abstract:
At first, we recall the basic concept, By a
residual lattice is meant an algebra
L = (L,¡ý,¡ü,.,o,0,1) such that
(i) L = (L,¡ý,¡ü,0,1) is a bounded lattice,
(ii) L = (L,.,1) is a commutative monoid,
(iii) it satisfies the so-called adjoin ness property:
(x ¡ý y) . z = y if and only if y ¡Â z ¡Â x o y
Let us note [7] that x ¡ý y is the greatest element
of the set (x ¡ý y) . z = y
Moreover, if we consider x . y = x ¡ü y , then x o y
is the relative pseudo-complement of x with respect
to y, i. e., for . = ¡ü residuated lattices are just
relatively pseudo-complemented lattices. The
identities characterizing sectionally pseudocomplemented
lattices are presented in [3] i.e. the
class of these lattices is a variety in the signature
{¡ý,¡ü,o,1}. We are going to apply a similar
approach for the adjointness property:
