Situation calculus has been applied widely in artificial intelligence to model and reason about actions and changes in dynamic systems. Since actions carried out by agents will cause constant changes of the agents' beliefs, how to manage these changes is a very important issue. Shapiro et al. [22] is one of the studies that considered this issue. However, in this framework, the problem of noisy sensing, which often presents in real-world applications, is not considered. As a consequence, noisy sensing actions in this framework will lead to an agent facing inconsistent situation and subsequently the agent cannot proceed further. In this paper, we investigate how noisy sensing actions can be handled in iterated belief change within the situation calculus formalism. We extend the framework proposed in [22] with the capability of managing noisy sensings. We demonstrate that an agent can still detect the actual situation when the ratio of noisy sensing actions vs. accurate sensing actions is limited. We prove that our framework subsumes the iterated belief change strategy in [22] when all sensing actions are accurate. Furthermore, we prove that our framework can adequately handle belief introspection, mistaken beliefs, belief revision and belief update even with noisy sensing, as done in [22] with accurate sensing actions only.

Belief revision performs belief change on an agent's beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey's rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey's rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey's rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce most of Darwiche and Pearl's postulates.

When merging belief sets from different agents, the result is normally a consistent belief set in which the inconsistency between the original sources is not represented. As probability theory is widely used to represent uncertainty, an interesting question therefore is whether it is possible to induce a probability distribution when merging belief sets. To this end, we first propose two approaches to inducing a probability distribution on a set of possible worlds, by extending the principle of indifference on possible worlds. We then study how the (in)dependence relations between atoms can influence the probability distribution. We also propose a set of properties to regulate the merging of belief sets when a probability distribution is output. Furthermore, our merging operators satisfy the well known Konieczny and Pino-Perez postulates if we use the set of possible worlds which have the maximal induced probability values. Our study shows that taking an induced probability distribution as a merging result can better reflect uncertainty and inconsistency among the original knowledge bases.