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Self-extensional logics of formal inconsistency: Decidability and limits for paraconsistency — arXiv:2608.28443

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.28443
License (as archived): CC0-1.0
Archived: 2026-10-17T11:52:26.726Z
SHA-256 of the archived text: b76466f76baf7b2e8459bb5a9715e13ef39e67c1c3dfe5c52d1b1f828f9b7f69
Stable URL of this page: https://metraipolis.com/documento/dc_01cf64eabb02

How to cite

Self-extensional logics of formal inconsistency: Decidability and limits for paraconsistency — arXiv:2608.28443 — arXiv (en), https://arxiv.org/abs/2608.28443 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_01cf64eabb02 (Metraipolis archive dc_01cf64eabb02, sha256 b76466f76baf7b2e8459bb5a9715e13ef39e67c1c3dfe5c52d1b1f828f9b7f69)

BibTeX

@misc{dc01cf64eabb02,
  title = {Self-extensional logics of formal inconsistency: Decidability and limits for paraconsistency — arXiv:2608.28443},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.28443},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_01cf64eabb02; sha256 b76466f76baf7b2e8459bb5a9715e13ef39e67c1c3dfe5c52d1b1f828f9b7f69},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.28443. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-31 in cs.LO).
Categorie arXiv: Logic in Computer Science (cs.LO).
Pagina del lavoro: https://arxiv.org/abs/2608.28443 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T11:27:04.109Z dalla pagina https://arxiv.org/catchup/cs.LO/2026-08-31?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).