In this thesis we consider access control logics and checking conformance for regulatory documents, together. In chapter 3, operator says is represented with notion “saying” for access control. Here, says is a modal with the system K , and it is idempotent, commutative, and associative. In chapter 5, regulatory conformance is considered. There is a system with some principals and predicates, and many laws. There is maybe a body of regulations that has complex reference. A system has conformance if obligations are satisfied. The conformance checking needs reasoning for determining obligations. This reasoning is non-monotonic and for a state of predicates, and a body of regulations might have several possible worlds. There is an algorithm for computing these possible worlds, and these possible worlds are called fixed points; because they are arose from using an inflationary function, and these possible worlds are its fixed points. In chapter 6, an interaction between “saying” and formalization of regulatory documents is expressed. There is an axiomatize for this interaction and its reasoning. Its semantics is upon Kripke’s semantics. This logic is called “Permission to Speak” and for it, theorems “soundness”, “completeness”, and “decidability” are proved. In this thesis, we consider “Paradox of the Court” that is between Protagors and his student Euathlus. We try to study this paradox in this approach, by our formalization in this logic (Permission to Speak). It seems that this logic can be equipped with quantification over formulas in future works for giving a better formalization for this paradox.
