Objects, Types and Modal Logics

Abstract

In this paper we present a modal logic for describing properties of
terms in the object calculus of Abadi and Cardelli [AC96]. The logic is
essentially the modal mu-calculus of [Koz83]. The fragment allows us
to express the temporal modalities of the logic CTL [BAMP83]. We
investigate the connection between the type system Ob_1<:mu and the
mu-calculus, providing a translation of types into modal formulae and
an ordering on formulae that is sound w.r.t. to the subtype ordering
of Ob_1<:mu.