  We formally investigate immediate and mediate grounding operators from an
inferential perspective. We discuss the differences in behaviour displayed by
several grounding operators and consider a general distinction between
grounding and logical operators. Without fixing a particular notion of
grounding or grounding relation, we present inferential rules that define, once
a base grounding calculus has been fixed, three grounding operators: an
operator for immediate grounding, one for mediate grounding (corresponding to
the transitive closure of the immediate grounding one) and a grounding tree
operator, which enables us to internalise chains of immediate grounding claims
without loosing any information about them. We then present an in-depth
proof-theoretical study of the introduced rules by focusing, in particular, on
the question whether grounding operators can be considered as logical operators
and whether balanced rules for grounding operators can be defined.
