We present a novel and highly automated technique for dynamic system level power management of System-on-aChip (SoC) designs. We present a formal system to represent power constraints and power intent as rules. We also present a Term Rewriting Systems based rule rewriting engine as our dynamic power manager. We provide a notion of formal correctness of our rule engine execution and provide a robust algorithm to dynamically and automatically manage power consumption in large SoC designs.There are two fundamental building blocks at the core of our technique. First, we present a powerful formal system to capture power constraints and power intent as rules. This is a selfchecking system and will automatically flag conflicting constraints or rules. Next, we present a rewriting strategy for managing power constraint rules using a formal deductive logic technique specially honed for dynamic power management of SoC designs. Together, this provides a common platform and representation to seamlesslycooperatebetweenhardwareandsoftwareconstraints to achieve maximum platform power optimization dynamically during execution.We demonstrate our technique in multiple contexts on an SoC design of the state-of-the-art next generation Intel smartphone platform.