A common requirement in policy specification languages is the ability to map policies to the underlying network devices. Doing so, in a provably correct way, is important in a security policy context, so administrators can be confident of the level of protection provided by the policies for their networks. Existing policy languages allow policy composition but lack formal semantics to allocate policy to network devices. Our research tackles this from first principles: we ask how network policies can be described at a high-level, independent of firewall-vendor and network minutiae. We identify the algebraic requirements of the policy mapping process and propose semantic foundations to formally verify if a policy is implemented by the correct set of policy-arbiters. We show the value of our proposed algebras in maintaining concise network-device configurations by applying them to real-world networks.