Revising Partial Pre-Orders with Partial Pre-Orders: A Unit-Based Revision Framework

Belief revision studies strategies about how agents revise their belief states when receiving new evidence.  Both in classical belief revision and in epistemic revision, a new input is either in the form of a (weighted) propositional formula or a total pre-order (where the total pre-order is considered as a whole).  However, in some real-world applications, a new input can be a partial pre-order where each unit that constitutes the partial pre-order is important and should be considered individually. To address this issue,  in this paper, we study how a partial pre-order representing the prior epistemic state can be revised by another partial pre-order (the new input) from a different perspective, where the revision is conducted recursively on the individual units of partial pre-orders.  We propose different revision operators (rules), dubbed the extension, match, inner and outer revision operators, from different revision points of view. We also analyze several properties for these operators.