30/04 - Rafael Testa

A system of Belief Revision based on the formal consistency operator

The Belief Revision studies how rational agents change their beliefs when they receive new information. The AGM system, most influential work in this area of study presented by Alchourrón, Gärdenfos and Makinson, postulates rationality criteria for different types of belief change and provides explicit constructions for such -- the equivalence between the postulates and operations is called the representation theroem. Recent studies show how the AGM paradigm can be compliant with different non-classical logics, which is called the AGM-compliance -- this is the case of the paraconsistent logics family that we analyzed, the Logics of Formal Inconsistency (LFIs).

Despite the AGM-compliance, when we consider a new logic its underlying rationality must be understood and its language should be used in fact. In this work, we redefine the AGM operations and propose new constructions, which actually captures the intuition of LFIs -- this is what we call the
AGM° system. Thus we provide an interesting interpretation for these logics, more in line with formal epistemology. In an alternative approach, by considering the AGM-compatibility, the AGM results can be directly applied to LFIs (as we presented in the previous seminar). In both approaches, we prove the corresponding theorems of representation where needed.

This is part of my doctoral thesis supervised by Professor Dr. Marcelo Esteban Coniglio (Unicamp) and by Professor Dr. Márcio Moretto Ribeiro (USP).