AGM-Style Revision of Beliefs and Intentions

We introduce a logic for temporal beliefs and intentions based on Shoham’s database perspective and we formalize his coherence conditions on beliefs and intentions. In order to do this we separate strong beliefs from weak beliefs. Strong beliefs are independent from intentions, while weak beliefs are obtained by adding intentions to strong beliefs and everything that follows from that. We provide AGM-style postulates for the revision of strong beliefs and intentions: strong belief revision may trigger intention revision, but intention revision may only trigger revision of weak beliefs. After revision, the strong beliefs are coherent with the intentions. We show in a representation theorem that a revision operator satisfying our postulates can be represented by a pre-order on interpretations of the beliefs, together with a selection function for the intentions.