2019/12/21 by Marcelo E. Coniglio, Coniglio, Marcelo E., Aldo Figallo-Orellano +3
Computer Science · #Advanced Algebra and Logic #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.1912.10277
openalex publication_date 2019/12/21 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28
The logics of formal inconsistency (LFIs, for short) are paraconsistent\nlogics (that is, logics containing contradictory but non-trivial theories)\nhaving a consistency connective which allows to recover the ex falso quodlibet\nprinciple in a controlled way. The aim of this paper is considering a novel\nsemantical approach to first-order LFIs based on Tarskian structures defined\nover swap structures, a special class of multialgebras. The proposed semantical\nframework generalizes previous aproaches to quantified LFIs presented in the\nliterature. The case of QmbC, the simpler quantified LFI expanding classical\nlogic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o\nis also studied, which is equivalent to the quantified version of da Costa and\nD'Ottaviano 3-valued logic J3. The semantical structures for this logic turn\nout to be Tarkian structures based on twist structures. The expansion of QmbC\nand QLFI1o with a standard equality predicate is also considered.\n