Abduction is the problem of finding the best explanation for a given set of observations. Within Al, this has been modeled as proving the observation by assuming some set of hypotheses. Cost-based abduction associates a cost with each hypothesis. The best proof is the one which assumes the least costly set. Previous approaches to finding the least cost set have formalized cost-based abduction as a heuristic graph search problem. However, efficient admissible heuristics have proven difficult to find. In this paper, we present a new technique for finding least cost sets by using linear constraints to represent causal relationships. In particular, we are able to recast the problem as a 0-1 integer linear programming problem. We can then use the highly efficient optimization tools of operations research yielding a computationally efficient method for solving cost-based abduction problems. Experiments comparing our linear constraint satisfaction approach to standard graph searching methodologies suggest that our approach is superior to existing search techniques in that our approach exhibits an expected-case polynomial run-time growth rate.
