Embedding alternating-time temporal logic in strategic STIT logic of agency

Seeing To It That (STIT) logic is a logic of agency, proposed in the 1990s in the domain of philosophy of action. It is the logic of constructions of the form 'agent a sees to it that phi'. We believe that STIT theory can contribute to the logical analysis of multiagent systems. To support this claim, we show that there is a close relationship with more recent logics for multiagent systems. This work extends Broersen et al. (2006, Electron Notes Theor. Comput. Sci., Vol. 157, pp. 23-35) where we presented a translation from Pauly's Coalition Logic to Chellas' STIT logic. Here we focus on Alur, Henzinger and Kupferman's Alternating-time Temporal Logic (ATL), and the logic of the 'fused' lozenge(s)[_scstit :_] operator for strategic ability, as described by Horty. After a brief presentation of ATL and the definition of a discrete-time strategic STIT framework slightly adapted from Horty, we give a translation from ATL to the STIT framework, and prove that it determines correct embedding.