Information Technology Reference
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a
→
∀
outgoing arrow from each state for each
In fact, we only need one and only one
ʣ
since all the
a
a
→
∀
targeting sets can be intersected together, and the 'default'
transition would be
s
a
∈
→
∀
S
where
S
is the set of all possible states. Note that, in
general, the above requirements may help to bring back the missing reasoning power
within the scope of
K
,due to the lack of necessitation rule for
K
in the logic.
To conclude, our epistemic framework is more compact and constructive compared
to the standard possible-world approach of epistemic logic, in the sense that the hyper
model resembles a collection of Kripke models and we can incrementally extend the
model even from scratch by adding new imprecise information. At the same time, we
pay the price that we are not able to represent all the collections of Kripke models since
certain dependency of transitions is not encoded in the hyper models. To use the logic,
we may make use of the 3-valued model checking algorithms (e.g., [6]), we leave out
the exact complexity analysis to future work. Finally, it is also a natural next step to go
probabilistic, as probabilities can be seen as another form of abstraction of qualitative
information, as remarked in [8].
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