A Logic for Paraconsistent Belief Revision based on Epistemic Entrenchment
Marcelo E. Coniglio, Martin Figallo, Rafael R. Testa
TL;DR
Problem: extend AGM-style belief revision to paraconsistent settings by integrating epistemic entrenchment within Logics of Formal Inconsistency ($LFI$). Approach: introduce two logics, $Cbr$ and $RCbr$, with $RCbr$ self-extensional and grounded in $Nmatrices$ semantics and BALFIs, and develop contraction via an epistemic-entrenchment ordering within an $AGM\circ$ framework over $RCbr$. Contributions: demonstrate that $RCbr$ is capable of expressing replacement and contains a countermodel showing that schemas $(cp1)$–$(cp4)$ may fail, derive extensional contraction postulates, and relate strong epistemic attitudes to entrenched beliefs; establish how entrenchment yields a principled contraction operator via $(G\div)$ and connect results to $RCie$ where $\circ\circ\alpha$ is a theorem. Significance: extends classical belief revision to paraconsistent knowledge bases, enabling robust belief dynamics in inconsistent domains such as multi-agent systems, with semantic grounding via $Nmatrices$ and BALFIs, and points to future work on revision, semi-revision, and practical applications in inconsistent knowledge bases.
Abstract
This paper addresses the integration of epistemic entrenchment into paraconsistent belief revision systems based on Logics of Formal Inconsistency (LFIs). While systems like AGMp and AGMo adapt AGM principles to paraconsistency, they lack mechanisms to rank beliefs, primarily due to the absence of properties such as the replacement property in the underlying logics. We introduce two novel logics, Cbr and RCBr, with the latter extending the former to fully address these limitations given that it is self-extensional. Using RCBr, we define contraction operations via epistemic entrenchment, adhering to key rationality principles. Our framework leverages non-deterministic matrix semantics (Nmatrices) and Boolean algebras with LFI operators (BALFIs), providing a robust foundation for paraconsistent reasoning. These contributions advance the theory of paraconsistent belief revision and pave the way for applications in domains such as multi-agent systems and inconsistent knowledge bases.