Abductive Reasoning, Belief Expansion and Nonmonotonic Cesequence

When dealing with a situation in which new information is to be incorporated into an epistemic state, most belief revision frameworks, including the AGM, incorporate solely this new information. A more natural proposal is that the agent seeks some explanation or justification first and attempts to incorporate the new information together with its justification into the agent’s current epistemic state. Pagnucco, Nayak and Foo model this proposal by developing a belief change operator known as abductive expansion which adds abductive inference to the belief expansion process. They develop rationality postulates for abductive belief expansion and provide a construction in terms of selection functions. However, this account lacks a proper semantic treatment. In this paper we present a formal sphere semantics for abductive expansion. By imposing an ordering over the possible worlds that are consistent with current beliefs we demonstrate a method for selecting those worlds consistent with the abductively expanded epistemic state. We also investigate an epistemic entrenchment style ordering over formulae which can be used to determine those formulae to be incorporated into the new epistemic state. This ordering has important consequences for expectation orderings and nonmonotonic inference. Using observations first made by Gärdenfors & Makinson and Williams we indicate how this entrenchment may be used for default reasoning. We also translate the abductive expansion postulates into conditions on a nonmonotonic consequence relation j .