The Quali cation Problem - Challenges for Action Theories - page 85

then any observation entailed by O 1 is also entailed by O 2 . This is a conse-
quence of the fact that adding observations only reduces the set of models.
A fundamental task when addressing the Qualication Problem is therefore
to modify an underlying monotonic entailment relation so as to become a
nonmonotonic one.

3.2 Minimizing Abnormal Disqualications

Recall from above the scenario where the only observation concerns the en-
gine, stating that it is not running. No information is given as to whether the
tail pipe is clogged or not. According to our action theory, the set of models
of this scenario divides into two classes, one of which consists in all models
which consider initially false fluent

), while the models of the other
class consider that fluent true. Suppose somewhere in the underlying domain
specication it is said that

(

in pt

unex-
ecutable even if all regular preconditions are satised. Then half the models
entail this very conclusion, i.e., that the action cannot be performed, the
others do not so. Hence, if all models need to be taken into account when de-
ciding on entailment, then nothing follows from the given observations as to
the action in question being executable. As argued in the introduction to the
Qualication Problem, however, it is reasonable to conclude, by default, that
starting the engine is possible. Granting this conclusion therefore requires to
ignore all those models which claim the contrary.
Dubious and unsound as it may seem to simply disregard `inconvenient'
models preventing the desired conclusion there is good reason for so doing in
this particular situation. It has been said that an abnormal disqualication
should be assumed away by default, that is, as long as this assumption is
consistent with the available information. From the model perspective, this
amounts to disregarding all models which entail an abnormal action disqual-
ication if only at least one model exists of the scenario at hand where this
abnormality does not hold. One way of achieving this formally is to introduce
a so-called preference criterion. Being a partial order on models, this criterion
will allow us to select the most preferred ones and, then, to conne ourselves
to those when talking about entailment.
The concept of model preference is inherently nonmonotonic, just as the
Qualication Problem requires it. Additional observations may invalidate
some of the models, among which, moreover, might be all previously pre-
ferred ones. As a consequence, models that have been disregarded earlier
may now come to light and give rise to a very dierent set of entailed formu-
las. Recall our example where we add to :

in ( pt ) being true renders action ignite

after [ ] the observation that
there is a potato in the tail pipe initially, i.e., in ( pt ) after [ ]. This new infor-
mation falsies every model that claims the possibility to ignite the engine.
The remaining, previously unpreferred models all suggest an abnormal dis-
qualication of the action, hence do now entail ignite inexecutable after [],
as we will note this kind of observation:

runs