By David Cooper, William Polk, Andrew Regenscheid, Murugiah Souppaya

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Different types of mathematical logics are available such as Propositional logic, first-order logic, modal logic, etc. Each of these logics can express different types of concepts along with precise semantics to capture these concepts. For example, Propositional logic allows to express relationship among sentences using sentential connectives, first order logic, in addition to the capabilities of Propositional logic, allows to express the fine grained structure that exists within each of the sentences, and modal logic allows to model action, temporal, spatial, deontic, and other such concepts.

Journal of ACM, 55(1), 1–42. Harel, D. (1979). First-Order Dynamic Logic. , Secaucus, NJ, USA. , & Walter, T. (2007, September). A Policy Language for Distributed Usage Control. In Proceedings of the 12th European Symposium On Research 19 Rights Expression Languages In Computer Security, pages 531–546, Dresden, Germany. , & Schallhart, C. (2004). Towards Formal Semantics for ODRL. In ODRLWorkshop, pages 137–148, Vienna, Austria. , & Ryan, M. (2000). Logic in Computer Science: Modelling and Reasoning about Systems.

A combination of predicates along with quantifiers allows Predicate logic to capture the semantics of statement x which says that Alice is a user. The expressive power of First Order Predicate logic is much greater than Propositional logic, and can capture the semantics of complex statements such as: All members of group “grp” can play song “hotelClifornia” on all the devices in the authorized domain “home”. Alice is a member of group “grp”. Device “dev” belongs to the domain “home”. The above group of statements can be captured in Predicate logic, and it can be mathematically 15 Rights Expression Languages proved that Alice can play song hotelCalifornia on device dev.

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