Recent work in network security has focused on the fact that combinations of exploits are the typical means by which an attacker breaks into a network. Researchers have proposed a variety of graph-based analysis approach, and there is often a lack of logical formalism. This paper describes a new approach to represent and analyze network vulnerability. We propose logical exploitation graph, which directly illustrate logical dependencies among exploitation goals and network configure. Our logical exploitation graph generation tool builds upon LEG-NSA, a network security analyzer based on Prolog logical programming. We demonstrate how to reason all exploitation paths using bottom-up and top-down evaluation algorithms in the Prolog logic- programming engine. We show experimental evidence that our logical exploitation graph generation algorithm is very efficient.