MODELING CYCLICITY AND GENERALIZED COST-BASED ABDUCTION USING LINEAR CONSTRAINT SATISFACTION

Abductive reasoning (explanation) is a backward-chaining process on a collection of logical rules. Cost-based abduction is a model for abductive reasoning which provides a concrete formulation of the explanation process. Unfortunately, abduction is an NP-hard task. Current approaches for performing abductive reasoning have been based on graph searching heuristics. However, they are very restrictive and still exhibit expected-case exponential growth rates. One particularly stringent restriction can be found in cost-based abduction whereby the knowledge base must be acyclic. The existence of cyclicity results in anamolous behaviour. In this paper, we present an extended model called generalized cost-based abduction for general knowledge bases. We provide two approaches for solving this model by using a recently introduced technique different from graph searching. This technique uses linear constraints to flexibly represent our knowledge. The problem can then be recast into 0-1 integer linear programming. The flexibility of the new representation scheme can be naturally exploited to handle cyclicity. Our first approach is based on explicitly identifying each reasoning cycle. The second is somewhat more general and based on graph topology. Each approach provides different strengths depending on the abduction problem to be solved.