Reasoning about history based access control policy using past time operators of interval temporal logic
Interval Temporal Logic (ITL) is a flexible notation for the propositional and first-order logical reasoning about periods of time that exist in specifications of hardware and software systems. ITL is different from other temporal logics since it can deal with both sequential and parallel composition and provides powerful and extensible specification and verification methods for reasoning about properties such as safety, time projection and liveness. Most imperative programming constructs can be seen as ITL formula that form the basis of an executable framework called Tempura that is used for the development and testing of ITL specifications.\\ ITL has only future operators, but the use of past operators make specifications referring to history more succinct; that is, there are classes of properties that can be expressed by means of much shorter formulas. What is more, statements are easier to express (simplicity) when past operators are included. Moreover, using past operators does not increase the complexity of interval temporal logic regarding the formula size and the simplicity. This thesis introduces past time of interval temporal logic where, instead of future time operators Chop, Chopstar, and Skip, we have past operators past Chop, past Chopstar and past Skip. The syntax and semantics of past time ITL are given together with its axiom and proof system. Furthermore, Security Analysis Toolkit for Agents (SANTA) operators such always-followed-by and the strong version of it has been given history based semantics using past time operators. In order to evaluate past time interval temporal logic, the problem of specification, verification of history based access control policies has been selected. This problem has already been solved using future time of interval temporal logic ITL but the drawback is that policy rules are not succinct and simple. However, the use of past time operators of ITL produces simple and succinct policy rules. The verification technique used to proof the safety property of history based access control policies is adapted for past time ITL to show that past time operators of interval temporal logic can specify and verify a security scenario such as history based access control policy.
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