Three Scenarios for the Revision of Epistemic States

Abstract

This position paper discusses the difficulty of interpreting iterated belief revision in the scope of the existing literature. Axioms of iterated belief revision are often presented as extensions of the AGM axioms, upon receiving a sequence of inputs. More recent inputs are assumed to have priority over less recent ones. We argue that this view of iterated revision is at odds with the claim, made by Gärdenfors and Makinson, that belief revision and non-monotonic reasoning are two sides of the same coin. We lay bare three different paradigms of revision based on specific interpretations of the epistemic entrenchment defining an epistemic state and of the input information. If the epistemic entrenchment stems from default rules, then AGM revision is a matter of changing plausible conclusions when receiving specific information on the problem at hand. In such a paradigm, iterated belief revision makes no sense. If the epistemic entrenchment encodes prior uncertain evidence and the input information is at the same level as the prior information and possibly uncertain, then iterated revision reduces to prioritized merging. A third problem is one of the revision of an epistemic entrenchment by means of another one. In this case, iteration makes sense, and it corresponds to the revision of a conditional knowledge base describing background information by the addition of new default rules.

Rational Partial Choice Functions and Their Application to Belief Revision

“…Instead, here we assume a given agent's belief structure, to which every new piece of information is applied separately so as to derive a different new belief state. This is in line with the view of belief revision as defeasible inference discussed in [12,14], one of the three kinds of belief revision perspectives.…”

Using Transfinite Ordinal Conditional Functions

“…Iterated belief revision operators [3] do not allow to incorporate more and more recent observations, but more and more reliable observations. This subject is the starting point of the two interesting papers [9,4], where it is clearly explained that if one wants to incorporate more and more recent information, one has to use prioritised belief merging. Roughly, if the observations incorporation order depends only of recency, and that they can have different reliability, then just store the observations with their degree of reliability, and merge all those observations.…”

“…Roughly, if the observations incorporation order depends only of recency, and that they can have different reliability, then just store the observations with their degree of reliability, and merge all those observations. In [4] Dubois identifies three different kinds of revision. We will focus on the two first ones.…”

“…without giving them an "ontology") [6]. We think that the papers of Dubois [4] and Delgrande-Dubois-Lang [9] is an interesting reminder of this discussion for iterated belief change.…”

“…So to sum up Dubois' view in [4], consider that the agent epistemic state is represented by two bases: a base of rules and a base of facts, the base of rules being more important/reliable/entrenched than the base of facts. Then the two kinds of revision are defined by the base that has to be revised.…”