A Linear Constraint Satisfaction Approach to Cost - BasedAbduction 1

Abduction is the problem of nding the best explanation for a given set of observations. Within AI, 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 nding the least cost set have formalized cost-based abduction as a heuristic graph search problem. However, eecient admissible heuristics have proven diicult to nd. In this paper, we present a new technique for nding 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 eecient optimization tools of operations research yielding a computationally eecient 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. This paper extends and improves the earlier work presented in 15,16]. Special thanks to Eugene Charniak for important pointers and critical review of this paper. Also, thanks to the anonymous reviewers whose suggestions improved this paper.