A Semantic Account of Iterated Belief Revision in the Situation Calculus

Recently Shapiro et al. explored the notion of iterated belief revision within Reiter's version of the situation calculus. In particular, they consider a notion of belief defined as truth in the most plausible situations. To specify what an agent is willing to believe at different levels of plausibility they make use of so-called belief conditionals, which themselves neither refer to situations or plausibilities explicitly. Reasoning about such belief conditionals turns out to be complex because there may be too many models satisfying them and negative belief conditionals are also needed to obtain the desired conclusions. In this paper we show that, by adopting a notion of only-believing, these problems can be overcome. The work is carried out within a modal variant of the situation calculus with a possible-world semantics which features levels of plausibility. Among other things, we show that only-believing a knowledge base together with belief conditionals always leads to a unique model, which allows characterizing the beliefs of an agent, after any number of revisions, in terms of entailments within the logic.