A framework for linear authorization logics

Linear authorization logics (LALs) are logics based on linear logic that can be used for modeling effect-based authentication policies. LALs have been used in the context of the Proof-Carrying Authorization framework, where formal proofs must be constructed in order for a principal to gain access to some resource elsewhere. This paper investigates the complexity of the provability problem, that is, determining whether a formula is provable in a linear authorization logic. We show that the multiplicative propositional fragment of LAL is already undecidable in the presence of two principals. On the other hand, we also identify a first-order fragment of LAL for which provability is PSPACE-complete. Finally, we argue by example that the latter fragment is natural and can be used in practice.