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Knowing Why - On the Dynamics of Knowledge about Actual Causes in the Situation Calculus

Reasoning about observed effects and their causes is important in many applications. For instance, understanding why a plan failed can aid the task of replanning by allowing the agent to tailor a better plan. But under incomplete information, an agent may be unable to determine which actions/events caused an effect. To overcome this, the agent may be able to perform some sensing actions that allow him to figure out what caused the effect. This becomes even more important in multiagent contexts, where an agent may want to identify which agents caused some effect, or possibly prevent other agents from determining who caused something. The effects involved may even be epistemic effects, such as an agent coming to know the PIN of a bank card, and the causes may be sensing actions. Reasoning about such causes is a key part of "theory of mind" and understanding other agents’ behaviour. While there has been much work on causality from an objective standpoint, causality from the point of view of individual agents has received much less attention. In this paper, we develop a formalization of knowledge about actual causes in the situation calculus, and how it is affected by actions including sensing. We show that the proposed framework has some intuitive properties and study the conditions under which an agent can be expected to come to know the causes of an effect.