An Extended Paradefinite Logic Combining Conflation, Paraconsistent Negation, Classical Negation, and Classical Implication: How to Construct Nice Gentzen-type Sequent Calculi

[jean-yves beziau]

Logica Universalis Webinar, August 3rd at 4pm CET
Speaker:   Norihiro Kamide (Teikyo University, Japan)
Title: An Extended Paradefinite Logic Combining Conflation, Paraconsistent
Negation, Classical Negation, and Classical Implication: How to Construct
Nice Gentzen-type Sequent Calculi
Abstract: In this study, an extended paradefinite logic with classical
negation (EPLC), which has the connectives of conflation, paraconsistent
negation, classical negation, and classical implication, is introduced as a
Gentzen-type sequent calculus. The logic EPLC is regarded as a modification
of Arieli, Avron, and Zamansky’s ideal four-valued paradefinite logic (4CC)
and as an extension of De and Omori’s extended Belnap–Dunn logic with
classical negation (BD+) and Avron’s self-extensional four-valued
paradefinite logic (SE4). The completeness, cut-elimination, and
decidability theorems for EPLC are proved and EPLC is shown to be
embeddable into classical logic. The strong equivalence substitution
property and the admissibilities of the rules of negative symmetry,
contraposition, and involution are shown for EPLC. Some alternative simple
Gentzen-type sequent calculi, which are theorem-equivalent to EPLC, are
obtained via these characteristic properties.
https://link.springer.com/article/10.1007/s11787-022-00305-9

Everybody is welcome to join. Registrate here:
https://www.springer.com/journal/11787/updates/20065848

Jean-Yves Beziau
Editor-in-Chief Logica Universalis
Organizer Logica Universalis Webinar
http://www.jyb-logic.org/
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