The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous approaches to quantified LFIs presented in the literature. The case of QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called |$\textbf{QLFI1}_\circ $| is also studied, which is equivalent to the quantified version of da Costa and D’Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and |$\textbf{QLFI1}_\circ $| with a standard equality predicate is also considered.

中文翻译：

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一阶交换结构语义，用于形式不一致的某些逻辑

形式上不一致的逻辑（简称LFI）是具有一致性连接词的超一致逻辑（即包含矛盾但非平凡的理论的逻辑），它允许以受控方式恢复极端法定的原则。本文的目的是考虑一种基于交换结构定义的Tarskian结构的一阶LFI的新颖语义方法，交换结构是一类特殊的多元代数。所提出的语义框架概括了文献中提出的量化LFI的先前方法。将详细分析QmbC的情况，即更简单的量化LFI扩展经典逻辑。QmbC的公理扩展称为| $ \ textbf {QLFI1} _ \ circ $ | 还研究了，等效于da Costa和D'Ottaviano 3值逻辑J3的量化版本。该逻辑的语义结构原来是基于扭曲结构的Tarkian结构。QmbC和| $ \ textbf {QLFI1} _ \ circ $ |的扩展 标准相等谓词也被考虑。