Abductive reasoning through filtering
Chitta Baral.
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 {\em abductive reasoning}.
Given a theory and some observations, by {\em 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 show it
to be equivalent to filter entailment
under less restrictive conditions.