Release Logics for Temporalizing Dynamic Logic

Abstract

Time and action are the two modalities which are combined in one logical system in this paper, in order to allow the partial specification of systems. In any composition of dynamic and temporal logic there is mutual interference. The dynamical component takes time and the temporal component should have an effect on the state space. The plain union of both logics cannot handle the mutual interference properly. After a discussion on the interference of action and temporal components, a multi-modal S5 logic, called Release Logic, is introduced to act as an orthogonalizing intermediate logic. With the now three modal components, two different temporal logics will be constructed. One logic allows instantaneous actions only and the other logic allows actions which take some time to complete.Release Logic can be viewed as the logic of controlled ignorance. It is a modal logic which is particularly well-fitted for partial specifications. Several specifications will be presented, most of them as one-liners.