Construction of revisions by explanations

Abstract

Belief Revision systems are logical frameworks to modeling the dynamics of knowledge. That is, how to modify our beliefs when we recieve new information. The main problem arises when the information is inconsistent with beliefs that represents our epistemic state. For instance, suppose we believe that a Ferrari coupe is the fastest car and then, we found that some Porsche car are faster than Ferrari cars. Surely, we need to revise our beliefs in order to accept the new information preserving as much old information as possible. There are many different models for belief revision but AGM is the most popular one. Almost any others are based on the foundations of AGM. They present an epistemic model (the formalism in which the beliefs will be represented) and then define different kinds of operator. The basic representation of epistemic states is trough belief sets (set of sentences closed under logical consequence) or belief bases (set of sentences not necessarily closed). Each operator may be represented in two ways: rationality postulates to be satisfied. Rationality postulates determine constraints that the respective operators should satisfy. They treat the operators as black boxes; after receiving certain inputs (of new information) we know what the response will be but not the internal mechanisms used. The operators for change use selection functions to determine which beliefs will be erased from epistemic state. Partial meet contarctions (AGM model) are based on a selection among subsets of the original set that do not imply the information to be retracted. The kernel contarction approach is based on a selection among the sentences that imply the information to be retracted. Revision operators can be defined through Levi identity; in order to revise an epistemic state K with respect to a sentence (, we contract with respect (( and then expand the new set with respect to (. On the other hand, consolidations are operators that make set of sentences (non closed under logical consequence) consistent. One of the most discussed properties of the revision operators is success. Success specifies that new information has primary over the beliefs of an agent. We propose a kind of non prioritized revision operator in which the new information is supported by an explanation. Each explanation is a set of sentences with some restrictions. The operator we propose is built in terms of kernel contractions and consolidations. This presentation contains several examples that justify the intuitions behind our model.