Backtracking actions are interesting for
the study of reasoning strategies. The
following axioms allow us to take into
account backtracking actions within our
formalization. Axiom 
describes two simple heuristics for
determining the appropriateness of
backtracking actions, i.e., for
detecting dead-ends during the
searching process. Backtracking
actions are taken when: (1) the
length
of the mental situation explored is
equal to some threshold N ; or (2) its length is
smaller than N but there are no
appropriate mental actions that can be
applied to it.
Figure: This figure illustrates the
definition of Path(m) in axiom
: 
,
, 
, and
.
It is possible to define more interesting heuristics for the appropriateness of backtracking actions, which detect early on unappropriate choices of the search strategy.
The path associated with a mental
situation m describes the sequence
of mental actions (including
backtracking actions of the form
Back) STRIPS needs to perform in
order to find m (see figure
for a graphical explanation).
Taking into account backtracking actions
(i.e., including axioms ,
and ) requires
modifying the definition of goal stack
derivation (axiom )
as follows.
