Evidence-Based Belief Revision for Non-Omniscient Agents
Kristina Gogoladze

Abstract:
It has long been recognized that inconsistencies may easily occur in people's beliefs in real life. Even if one is rational, one may hold inconsistent beliefs due to receiving conflicting information along with the fact that our limited capacity for information processing (or limited memory) may make it hard to spot the inconsistency. A rational agent would, of course, like to revise his beliefs when he becomes aware of an inconsistency. However, the usual discussion in the Belief Revision literature on solving the contradiction involving old evidence and new evidence assumes that the agent is always aware of this contradiction (because of his logical omniscience).
 
In this thesis, we propose a logic that allows an agent to hold inconsistent beliefs if he has not noticed that they are inconsistent. The logic allows the agent to reason consistently, even if there are inconsistencies in the agent's beliefs. Furthermore, if the agent becomes aware of the inconsistency, he is able to correct his beliefs so that they are no longer explicitly contradictory. We first give the semantics of the logic, and then present a sound and complete axiomatization for the proposed logic, forming a formal basis for holding and fixing inconsistent beliefs in a rational agent.