Taken from 'Belief Revision' (1992) (page 8), Edited by Peter Gardenfors
A question that has to be answered when modelling a state of belief is whether the justifications for the beliefs should be part of the model or not. With respect to this question there are two main approaches. One is the foundations theory which holds that one should keep track of the justifications for one's beliefs: Propositions that have no justification should not be accepted as beliefs. The other is the coherence theory which holds that one need not consider the pedigree of one's beliefs. The focus is instead on the logical structure of the beliefs - what matters is how a belief coheres with the other beliefs that are accepted in the present state.
It should be obvious that the foundations and the coherence theories have very different implications for what should count as rational changes of belief systems. According to the foundations theory, belief revision should consist, first, in giving up all beliefs that no longer have a satisfactory justification and, second, in adding new beliefs that have become justified. On the other hand, according to the coherence theory, the objectives are, first, to maintain consistency in the revised epistemic state and, second, to make minimal changes of the old state that guarantee sufficient overall coherence. Thus, the two theories of belief revision are based on conflicting ideas of what constitutes rational changes of belief. The choice of underlying theory is, of course, also crucial for how a computer scientist will attack the problem of implementing a belief revision system.
Taken from 'Automating Belief Revision for AgentSpeak' (2006), Natasha Alechina et al.
AGM style belief revision is sometimes referred to as coherence approach to belief revision, because it is based on the ideas of coherence and information economy. It requires that the changes to the agent's belief state caused by a revision be as small as possible. In particular, if the agent has to give up a belief in A, it does not give up believing in things for which A was the sole justification, so long as they are consistent with the remaining beliefs.
Another strand of theoretical work in belief revision is the foundational, or reason-maintenance style approach to belief revision. Reason-maintenance style belief revision is concerned with tracking dependencies between beliefs. Each belief has a set of justifications, and the reasons for holding a belief can be traced back through these justifications to a set of foundational beliefs. When a belief must be given up, sufficient foundational beliefs have to be withdrawn to render the belief underivable. Moreover, if all the justifications for a belief are withdrawn, then that belief itself should no longer be held. Most implementations of reason-maintenance style belief revision are incomplete in the logical sense, but tractable.
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