  Extensions of Answer Set Programming with language constructs from temporal
logics, such as temporal equilibrium logic over finite traces (TELf), provide
an expressive computational framework for modeling dynamic applications. In
this paper, we study the so-called past-present syntactic subclass, which
consists of a set of logic programming rules whose body references to the past
and head to the present. Such restriction ensures that the past remains
independent of the future, which is the case in most dynamic domains. We extend
the definitions of completion and loop formulas to the case of past-present
formulas, which allows capturing the temporal stable models of a set of
past-present temporal programs by means of an LTLf expression.
