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Abstract:
This paper investigates a family of logics for reasoning about the
dynamic activities and informational attitudes of agents,
namely the agents' beliefs and knowledge.
The logics are based
on a new formalisation and semantics
of the test operator of
propositional dynamic logic
and a representation of actions which
distinguishes abstract actions from concrete actions.
The new test operator, called informational test,
can be used to formalise the beliefs and knowledge of particular agents
as dynamic modalities.
This approach is consistent
with the formalisation
of the agents' beliefs and knowledge
as K(D)45 and S5 modalities.
Properties concerning informativeness, truthfulness and
preservation of beliefs
are proved for a derivative of the informational test operator.
It is shown that common belief and common knowledge
can be expressed in the considered logics.
This means,
the logics are more expressive
than propositional dynamic logic with
an extra modality for belief or knowledge.
The logics remain decidable and belong to 2EXPTIME.
Versions of the considered logics express natural additional properties
of beliefs or knowledge and interaction of beliefs or knowledge with
actions.
It is shown that a simulation of PDL can be constructed in one of these
extensions.