@ARTICLE{gargov93:_modal,
author = {G. Gargov and V. Goranko},
title = {Modal logic with names},
journal = {Journal of Philosophical Logic},
year = {1993},
volume = {22},
pages = {607--636},
number = {6},
abstract = { We investigate an enrichment of the propositional modal language
${\scr L}$ with a `universal' modality $\blacksquare$ having semantics
$x\vDash\blacksquare\phi$ iff $\forall y(y\vDash \phi)$, and a countable
set of `names'---a special kind of propositional variables ranging
over singleton sets of worlds. The obtained language ${\scr L}\sb
c$ proves to have great expressive power. It is equivalent with respect
to modal definability to another enrichment ${\scr L}\Boxed{\not=}$
of ${\scr L}$, where $\Boxed{\not=}$ is an additional modality with
the semantics $x\vDash\Boxed{\not=}\phi$ iff $\forall y(y\not= x\to
y\vDash\phi)$. Model-theoretic characterizations of modal definability
in these languages are obtained.
We also consider deductive systems in ${\scr L}\sb c$. Strong completeness
of the normal ${\scr L}\sb c$-logics is proved with respect to models
in which all worlds are named. Every ${\scr L}\sb c$-logic axiomatized
by formulae containing only names (but not propositional variables)
is proved to be strongly frame-complete. Problems concerning transfer
of properties such as [in]completeness, filtration, the finite model
property, etc. from ${\scr L}$ to ${\scr L}\sb c$ are discussed.
Finally, further perspectives for names in a multimodal environment
are briefly sketched. }
}