Abductive reasoning through filtering

Abstract

Abduction is an inference mechanism where given a knowledge base and some observations, the reasoner tries to find 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 filtering 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 filter entailment. In this paper we give necessary and sufficient conditions when abductive reasoning with respect to a theory and some observations is equivalent to the corresponding filter entailment. We then give sufficiency conditions for particular knowledge representation formalisms that guarantee that abductive reasoning can indeed be done through filtering and present examples from the knowledge representation literature where abductive reasoning is done through filtering. We extend the notions of abductive reasoning and filter 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 abductive reasoning and show the later to be equivalent to filter entailment under less restrictive conditions.