We introduce a new fragment
GF
2 +
of the first order logic — the two-variable guarded fragment with
one-way transitive guards. This logic corresponds in a natural way to temporal logics without past operators. We prove that the satisfiability
problem for
GF+
is
EXPSPACE-complete. The lower bound, obtained for the
monadic version of the considered logic without equality, improves
NEXPTIME lower bound for the whole two-variable guarded fragment with transitive guards
GF
2 +
TG, given by Szwast and Tendera [
8].