Information Technology Reference
In-Depth Information
4.4
Implementation
We implemented the tableau method for both
-semantics in Lotrec-
scheme [22]. The tool and the files for logics are available, respectively, at:
∩
-semantics and
ↆ
Appendix A.5 shows an output of Lotrecscheme.
5Con lu ion
We develop tableau system for both intersection and subset
PAL
based on monotone
modal logic. Here we present some problems for future work.
-
We m a y generalize ourtableau systems to the general dynamic epistemic logic set-
ting. Intersection
DEL
is already proposed in [31] and subset
DEL
is also proposed
in [17]. Our idea for developing tableau system for
PAL
sistotakefinitesequences
of public announcements into consider. In the
DEL
setting, we may consider his-
tories of actions in the action model. Thus we may develop the tableau rules for
operations as it is done in [1] for the
DEL
extension of modal logic
K
.
-
It is well-known that modal formulas corresponds to conditions on neighborhood
frames ([19]). Thus we may consider how tableau systems can be developed for ex-
tensions of monotone modal logic with additional modal axioms, and then consider
their dynamics extensions. The problem is to take those special frame conditions
into account in the tableau rules for modal operations.
-
As the satisfiability problems for both intersection and subset
PAL
are in NP,they
are reducible to the satisfiability problem for classical propositional logic [20]. We
aim at finding elegant reductions for obtaining e
cient solvers for both intersection
and subset
PAL
.
References
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/
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R.,
Halpern,
J.Y.:
Belief,
awareness,
and
limited
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Artificial Intelli-
gence 34(1), 39-76 (1988)
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Cambridge (1995)
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