Temporal alethic–deontic logic and semantic tableaux

The purpose of this paper is to describe a set of temporal alethic–deontic systems, i.e. systems that include temporal, alethic and deontic operators. All in all we will consider 2,147,483,648 systems. All systems are described both semantically and proof theoretically. We use a kind of possible world semantics, inspired by the so-called T × W semantics, to characterize our systems semantically and semantic tableaux to characterize them proof theoretically. We also show that all systems are sound and complete with respect to their semantics.