Paraconsistent Belief Revision: A Replacement-Enriched LFI for Epistemic Entrenchment

We further develop the formal foundations of Paraconsistent Belief Revision (PBR) by introducing Logics of Formal Inconsistency (LFIs) specifically designed to support the development of epistemic entrenchment-based models for belief change. The interpretation of formal consistency -- and, more broadly, of paraconsistency -- in terms of the epistemic attitudes adopted by rational agents and of these agents reasoning with potentially contradictory yet non-trivial epistemic states, respectively, is already well-established within the literature on PBR based on LFIs. However, previous approaches faced a key limitation: the absence of replacement in most LFIs prevented the construction of entrenchment-based operations. We address this gap by first revisiting and systematizing core properties essential for such modeling, formalizing them within Cbr, a previously introduced logic whose foundational properties we now examine and develop in depth. Building on this, we introduce RCbr, a replacement-enriched, self-extensional extension of Cbr, which makes it possible -- within an LFI-based framework -- to formally define epistemic entrenchment and to construct entrenchment-based belief revision mechanisms. This development enables a fully constructive approach to Belief Revision in paraconsistent settings, further advancing the theoretical treatment of LFIs and paraconsistency within the broader landscape of epistemic states and belief dynamics.