Abstract
I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided.
Highlights
The doxastic models constructed here are primarily aimed at reducing some of the idealisations that are common in the belief revision literature
I state some principles concerning the belief sets and belief revision, which fail in the proposed framework they are satisfied as axiom schemas or rules in some of the more common and well-known theories in the literature
The non-classical features of the revision framework principally follow from the underlying non-classical semantics
Summary
The doxastic models constructed here are primarily aimed at reducing some of the idealisations that are common in the belief revision literature. It has significantly influenced the succeeding works on belief revision especially in terms of the modelling idealisations mentioned above It is assumed in the AGM theory that belief sets, before and after the revisions, are closed under classical logical implication (by the closure postulate). The changes of belief take place on the belief bases This approach allows, for instance, agents to enjoy inconsistent pieces of information without having trivial belief sets (via the failures of various logical closure principles). I propose a model-shifting dynamic operation (together with its representation in the object language) to model belief revision via new information This operation is carried out on the possible collections of information that an agent has, rather than on the respective belief sets.
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