发表机构
Centre for Logic, Epistemology and the History of Science (CLE), University of Campinas (UNICAMP); Institute of Philosophy and the Humanities (IFCH), University of Campinas (UNICAMP)（坎皮纳斯大学逻辑、认识论与科学史中心; 坎皮纳斯大学哲学与人文学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究自扩展次协调逻辑RmbC的可判定性，分类一致性公理，识别爆炸性核心，证明其有限模型性质与可判定性，确定有效性问题的2-EXPTIME上界和coNP困难下界。
AI 中文摘要
RmbC是形式不一致性逻辑（LFIs）家族中的一种自扩展次协调逻辑，该系统通过添加两条全局推理规则从基础形式不一致性逻辑mbC中获得。RmbC以非爆炸否定¬和一致性算子∘为特征，可受控地恢复爆炸原理。RmbC及其主要公理扩展均承认标准林登鲍姆-塔尔斯基代数化，以带LFI算子的布尔代数（BALFIs）作为其代数语义。本文从RmbC出发，研究这种自扩展次协调行为可在公理层面延伸的程度：我们根据是否保留次协调性或导致经典坍缩对多组自然的一致性公理进行分类；识别出6个代数等价的爆炸性核心；分离出¬的排中律与对合否定组合的独立结构障碍。我们还首次研究了该自扩展形式不一致性逻辑家族的可判定性，作为首个结果，通过代数滤子证明了RmbC相对于BALFI语义的有限模型性质，该性质可推出可判定性，并将此结果推广到RmbC的多个次协调公理扩展。最后，我们确定RmbC的有效性问题的2-EXPTIME上界和coNP困难下界。
英文摘要
RmbC is a self-extensional paraconsistent logic in the family of Logics of Formal Inconsistency (LFIs). This system is obtained from mbC (the basic LFI) by adding the replacement property via two global inference rules. RmbC is characterized by a non-explosive negation $\neg$ and a consistency operator $\circ$, which recovers the principle of explosion in a controlled way. Together with its principal axiomatic extensions, RmbC admits a standard Lindenbaum-Tarski algebraization, with Boolean algebras with LFI operators (BALFIs) as its algebraic semantics. In this paper, we study how far this self-extensional paraconsistent behavior can be extended axiomatically, starting from RmbC. We classify pairs of very natural consistency axioms according to whether they preserve paraconsistency or force classical collapse; identify six minimal explosive combinations that collapse to a single algebraic core; and isolate a separate structural obstruction for the combination of excluded middle for $\neg$ with an involutive negation. We also investigate, for the first time, the decidability of this family of self-extensional LFIs. As a first result, we prove the finite model property for RmbC with respect to BALFI semantics via an algebraic filtration, which yields decidability, and transfer this result to several paraconsistent axiomatic extensions of RmbC. Finally, we establish a coNEXPTIME upper bound for the validity problem of RmbC and a coNP-hardness lower bound, and prove coNP-completeness for the principal extensions containing one of the six minimal explosive pairs.
CommentsRevised and expanded version. coNP-completeness was proved for the principal extensions containing at least one of the six minimal explosive pairs
