A Conditional Constructive Logic for Access Control and Its Sequent Calculus

Abstract

In this paper we study the applicability of constructive conditional logics as a general framework to define decision procedures in access control logics. To this purpose, we formalize the assertion A says φ, whose intended meaning is that principal A says that φ, as a conditional implication. We introduce $\textsf{Cond}_{\rm ACL}$, which is a conservative extension of the logic ICL recently introduced by Garg and Abadi. We identify the conditional axioms needed to capture the basic properties of the “says” operator and to provide a proper definition of boolean principals. We provide a Kripke model semantics for the logic and we prove that the axiomatization is sound and complete with respect to the semantics. Moreover, we define a sound, complete, cut-free and terminating sequent calculus for $\textsf{Cond}_{\rm ACL}$, which allows us to prove that the logic is decidable. We argue for the generality of our approach by presenting canonical properties of some further well known access control axioms. The identification of canonical properties provides the possibility to craft access control logics that adopt any combination of axioms for which canonical properties exist.