@ARTICLE{SchmidtTishkovsky08a,
AUTHOR = {Schmidt, R. A. and Tishkovsky, D.},
YEAR = {2008},
TITLE = {On Combinations of Propositional Dynamic Logic and Doxastic Modal Logics},
JOURNAL = {Journal of Logic, Language and Information},
VOLUME = {17},
NUMBER = {1},
PAGES = {109--129},
DOI = {http://dx.doi.org/10.1007/s10849-007-9041-6},
URL = {\url{http://www.cs.man.ac.uk/~schmidt/publications/SchmidtTishkovsky08a.html}},
ABSTRACT = {
We prove completeness and decidability results
for a family of combinations of 
propositional dynamic logic
and unimodal doxastic logics
in which the modalities may interact.
The kind of interactions we consider include three forms of commuting
axioms, namely, axioms similar to the axiom of perfect recall and the
axiom of no learning from
temporal logic, and a Church-Rosser axiom.
We investigate the influence
of the substitution rule
on the properties of these logics
and propose a new semantics
for the test operator to
avoid unwanted side effects
caused by the interaction of the classic test operator
with the extra interaction axioms.
}
}