Paraconsistent Belief Revision Based on a Formal Consistency Operator

Belief Revision studies how rational agents change their beliefs upon receiving new information. The AGM system, the most influential work in this area, investigated by Alchourrón, Gärdenfors, and Makinson, postulates rationality criteria for different types of belief changes and provides explicit constructions for them. The equivalence between the postulates and operations is called the representation theorem. Recent studies show how the AGM paradigm can be compliant with different non-classical logics, which is referred to as AGM-compliance. This is the case for the paraconsistent logics family we analyze in this thesis, known as the Logics of Formal Inconsistency (LFIs). Despite the AGM-compliance, when a new logic is considered, its underlying rationality must be understood, and its language should be used. In this way, new constructions are proposed, which accurately capture the intuition of LFIs – what we call the AGM◦ system. Thus, we provide a new interpretation for these logics, more aligned with formal epistemology. Alternatively, by considering AGM-compliance, we demonstrate how the AGM results can be directly applied to LFIs, resulting in the AGMp system. In both approaches, we prove the corresponding representation theorems where needed.