Intelligence Analysis Using Quantitative Preferences Davy Van Nieuwenborgh , Stijn Heymans, and Dirk Vermeir Dept. of Computer Science Vrije Universiteit Brussel, VUB Pleinlaan 2, B1050 Brussels, Belgium dvnieuwe,sheymans,dvermeir @vub.ac.be Abstract. The extended answer set semantics for simple logic programs, i.e. programs with only classical negation, allows for the defeat of rules to resolve contradictions. In addition, a partial order relation on the program’s rules can be used to deduce a preference relation on its extended answer sets. In this paper, we propose a “quantitative” preference relation that associates a weight with each rule in a program. Intuitively, these weights define the “cost” of defeating a rule. An extended answer set is preferred if it minimizes the sum of the weights of its defeated rules. We characterize the expressiveness of the resulting semantics and show how the semantics can be conveniently extended to sequences of weight preferences, without increasing the expressiveness. We illustrate an application of the approach by showing how it can elegantly express largest common sub- graph and subgraph isomorphic approximation problems, a concept often used in intelligence analysis to find similarities or specific regions of interest in large graphs of observed activity. 1 Introduction Over the last decade a lot of research has been done on declarative programming us- ing the answer set semantics [10, 2, 18], a generalization of the stable model semantics [8]. In answer set programming, one uses a logic program to modularly describe the requirements that must be fulfilled by the solutions to a particular problem, i.e. the an- swer sets of the program correspond to the intended solutions of the problem. One of the possible problems in answer set programming is the absence of any solutions in case of inconsistent programs. To remedy this, the authors proposed [16] the extended answer set semantics which allows for the defeat of problematic rules. E.g., the rules , and are clearly inconsistent and have no classical answer sets, while both and will be recognized as extended answer sets. Intuitively, is defeated by in , while defeats in . Within the context of inconsistent programs, it is natural to have some kind of pref- erence relation that is used to prefer certain extended answer sets above others. In [16], Supported by the FWO This work was partially funded by the Information Society Technologies programme of the European Commission, Future and Emerging Technologies under the IST-2001-37004 WASP project