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Concept
Belief revision
Summary
Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents.
What makes belief revision non-trivial is that several different ways for performing this operation may be possible. For example, if the current knowledge includes the three facts " is true", " is true" and "if and are true then is true", the introduction of the new information " is false" can be done preserving consistency only by removing at least one of the three facts. In this case, there are at least three different ways for performing revision. In general, there may be several different ways for changing knowledge.
Two kinds of changes are usually distinguished:
update the new information is about the situation at present, while the old beliefs refer to the past; update is the operation of changing the old beliefs to take into account the change;
revision both the old beliefs and the new information refer to the same situation; an inconsistency between the new and old information is explained by the possibility of old information being less reliable than the new one; revision is the process of inserting the new information into the set of old beliefs without generating an inconsistency.
The main assumption of belief revision is that of minimal change: the knowledge before and after the change should be as similar as possible. In the case of update, this principle formalizes the assumption of inertia. In the case of revision, this principle enforces as much information as possible to be preserved by the change.
The following classical example shows that the operations to perform in the two settings of update and revision are not the same. The example is based on two different interpretations of the set of beliefs and the new piece of information :
update in this scenario, two satellites, Unit A and Unit B, orbit around Mars; the satellites are programmed to land while transmitting their status to Earth; and Earth has received a transmission from one of the satellites, communicating that it is still in orbit.
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