Abductive reasoning through filtering

Abduction is an inference mechanism where given a knowledge base and some observations , the reasoner tries to nd hypotheses which together with the knowledge base explain the observations. A reasoning based on such an inference mechanism is referred to as abductive reasoning. Given a theory and some observations, by l-tering the theory with the observations, we mean selecting only those models of the theory that entail the observations. Entailment with respect to these selected models is referred to as lter entailment. In this paper we give necessary and suucient conditions when abductive reasoning with respect to a theory and some observations is equivalent to the corresponding lter entailment. We then give suuciency conditions for particular knowledge representation formalisms that guarantee that abductive reasoning can indeed be done through ltering and present examples from the knowledge representation literature where abductive reasoning is done through ltering. We extend the notions of abductive reasoning and lter entailment to allow preferences among explanations and models respectively and give conditions when they are equivalent. Finally, we give a weaker notion of abduction and show it to be equivalent to lter entailment under less restrictive conditions.