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We consider $S$-operations $f \colon A^{n} \to A$ in which each argument isassigned a signum $s \in S$ representing a "property" such as beingorder-preserving or order-reversing with respect to a fixed partial order on$A$. The set $S$ of such properties is assumed to have a monoid structurereflecting the behaviour of these properties under the composition of$S$-operations (e.g., order-reversing composed with order-reversing isorder-preserving). The collection of all $S$-operations with prescribedproperties for their signed arguments is not a clone (since it is not closedunder arbitrary identification of arguments), but it is a preclone with specialproperties, which leads to the notion of $S$-preclone. We introduce$S$-relations $\varrho = (\varrho_{s})_{s \in S}$, $S$-relational clones, and apreservation property ($f \mathrel{\stackrel{S}{\triangleright}} \varrho$), andwe consider the induced Galois connection${}^S\mathrm{Pol}$-${}^S\mathrm{Inv}$. The $S$-preclones and $S$-relationalclones turn out to be exactly the closed sets of this Galois connection. Wealso establish some basic facts about the structure of the lattice of all$S$-preclones on $A$.

$S$-preclones and the Galois connection ${}^S\mathrm{Pol}$-${}^S\mathrm{Inv}$, Part I