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Attack graphs are important tools for analyzing security vulnerabilities in enterprise networks. Previous work on attack graphs has not provided an account of the scalability of the graph generating process, and there is often a lack of logical formalism in the representation of attack graphs, which results in the attack graph being difficult to use and understand by human beings. Pioneer work by Sheyner, et al. is the first attack-graph tool based on formal logical techniques, namely model-checking. However, when applied to moderate-sized networks, Sheyner's tool encountered a significant exponential explosion problem. This paper describes a new approach to represent and generate attack graphs. We propose logical attack graphs, which directly illustrate logical dependencies among attack goals and configuration information. A logical attack graph always has size polynomial to the network being analyzed. Our attack graph generation tool builds upon MulVAL, a network security analyzer based on logical programming. We demonstrate how to produce a derivation trace in the MulVAL logic-programming engine, and how to use the trace to generate a logical attack graph in quadratic time. We show experimental evidence that our logical attack graph generation algorithm is very efficient. We have generated logical attack graphs for fully connected networks of 1000 machines using a Pentium 4 CPU with 1GB of RAM.