While logging events is becoming increasingly common in computing, in communication and in collaborative environments, log systems need to satisfy increasingly challenging (if not conflicting) requirements. In this paper we propose a high-level framework for modeling log systems, and reasoning about them. This framework allows one to give a high-level representation of a log system and to check whether it satisfies given audit and privacy properties which in turn can be expressed in standard logic. In particular, the framework can be used for comparing and assessing log systems. We validate our proposal by formalizing a number of standard log properties and by using it to review a number of existing systems. Despite the growing pervasiveness of log systems, we believe this is the first framework of this sort.