Semantic structures for one-stage and iterated belief revision

Semantic structures for belief revision and iterated belief revision are proposed. We start with one-stage revision structures that generalize the notion of choice function from rational choice theory. A correspondence between these one-stage structures and AGM belief revision functions is established. We then add branching time and consider more general structures that accommodate iterated revision. AGM temporal belief revision structures are defined and a syntactic axiomatization is provided

A conditional perspective of belief revision

Belief Revision is a subarea of Knowledge Representation and Reasoning (KRR) that investigates how to rationally revise an intelligent agent's beliefs in response to new information. There are several approaches to belief revision, but one well-known approach is the AGM model, which is rooted in work by Alchourrón, Gärdenfors, and Makinson. This model provides a set of axioms defining desirable properties of belief revision operators, which manipulate the agent's belief set represented as a set of propositional formulas. A famous extension to the classical AGM framework of Belief Revision is Darwiche and Pearl's approach to iterated belief revision. They uncovered that the key to rational behavior under iteration is adequate preservation of conditional beliefs, i.e., beliefs the agent is willing to accept in light of (hypothetical) new information. Therefore, they introduced belief revision operators modifying the agent's belief state, built from conditional beliefs. Kern-Isberner fully axiomatized a principle of conditional preservation for belief revision, which captures the core of adequate treatment of conditional beliefs during the revision. This powerful axiom provides the necessary conceptual framework for revising belief states with sets of conditionals as input, and it shows that conditional beliefs are subtle but essential for studying the process of belief revision. This thesis provides a conditional perspective of Belief Revision for different belief revision scenarios. In the first part, we introduce and investigate a notion of locality for belief revision operators on the semantic level. Hence, we exploit the unique features of conditionals, which allow us to set up local cases and revise according to these cases, s.t., the complexity of the revision task is reduced significantly. In the second part, we consider the general setting of belief revision with respect to additional meta-information accompanying the input information. We demonstrate the versatility and flexibility of conditionals as input for belief revision operators by reducing the parameterized input to a conditional one for two well-known parameterized belief revision operators who are similarly motivated but very different in their technical execution. Our results show that considering conditional beliefs as input for belief revision operators provides a gateway to new insights into the dynamics of belief revision

AGM-Like Paraconsistent Belief Change

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations