Pantelis Eleftheriou, Department of Pure Mathematics, University of Waterloo
“Model-theoretic constructions in many-valued modal logics”
We
study
a
family
of
Heyting-valued
modal
logics
introduced
by
Fitting
in
the
early
’90s.
For
each
logic
in
this
family,
the
semantics
is
given
via
Kripke-frames
whose
edges
are
labelled
with
values
from
an
underlying
Heyting
algebra
H.
If
H
is
finite,
the
semantics
corresponds
to
a
multiple-expert
semantics
of
interest
to
Knowledge
Representation,
where
every
value
of
H
defines
a
group
of
experts.
We
generalize
four
model-theoretic
constructions
from
modal
logic
to
this
setting
and
prove
truth-
invariance
results
under
these
constructions.
If
H
is
finite,
the
truth-invariance
results
correspond
to
invariance
of
the
epistemic
consensus
of
the
predefined
group
of
experts.
This
is
joint
work
with
C.
Koutras.