The Role of Abductive Reasoning within the Process of Belief Revision

An inquiring agent is concerned with obtaining as much new, error-free, information as possible. One way of doing this is to simply incorporate information presented to an agent as is. This strategy is adopted by many belief revision frameworks including the popular AGM framework. A more natural strategy would be for the agent to first seek an explanation or justification for the new information. After doing so, it could incorporate the explanation into its epistemic state together with the new information. Such a strategy would be particularly effective if the agent’s situation does not allow it to obtain new information easily. We model this strategy through the use of abductive reasoning. This allows us to then investigate the role of abductive inference within a belief revision framework based on the AGM. We not only look at the incorporation of new information but also at the removal of information. We begin by looking at some logical aspects of abduction and to contrast it, in a pragmatic sense, with the process of induction as performed by inverse resolution. We proceed to develop an account of an abductive expansion operator in the vein of the AGM framework. A definition, postulates and several constructions, reminiscent of the AGM, are developed together with a number of representation theorems. It is also shown how abductive expansion is related to nonmonotonic inference, in particular, default reasoning. The process of contraction is then investigated and we note how abduction can already be viewed as an active part of this operation. However, abductive expansion and AGM contraction do not exhibit the dual behaviour one might expect. This leads us into an investigation of an alternate operation known as Levi-contraction. We suggest a Grove style semantic modelling and provide additional postulates in order to obtain a complete characterisation. Our emphasis on expansion and contraction is guided to a large extent by Levi’s commensurability thesis which states that any revision can be achieved through a series of expansion and contraction operations. However, using our work on expansion and contraction, we briefly investigate the repercussions for an abductive revision operator determined through the Levi identity. It turns out that this problem relies heavily on that of iterated revision.