On subexponentials, focusing and modalities in concurrent systems

In this work we present the focused proof system SELLF⋒, which extends intuitionistic linear logic with subexponentials with the ability of quantifying over them, hence allowing for the use of an arbitrary number of modalities. We show that the view of subexponentials as specific modalities is general enough to give a modular encoding of different flavors of Concurrent Constraint Programming (CCP), a simple and powerful model of concurrency. More precisely, we encode CCP calculi capturing time, spatial and epistemic behaviors into SELLF⋒, thus providing a proof theoretic foundation for those calculi and, at the same time, setting SELLF⋒ as a general framework for specifying such systems.