A note on negation inconsistent variants of FDE-negation

  • H. Omori and H. Wansing introduced in a recent paper possible alternatives for the negation of the logic of first-degree entailment. One of their observations with regard to these alternative negations is that some of them turn out to induce negation inconsistency, meaning that some contradictions become provable (under an arbitrary premise) when used in place of the original negation. Omori and Wansing also considered a non-deterministic generalisation of such operators, but it was left open whether the generalised negation similarly induces negation inconsistency. In this paper, we provide an answer to this question in the positive, and moreover look into further generalisation and characterisation of non-deterministic operators which satisfy the formal criteria of negation inconsistency and its pair notion of negation incompleteness in the setting of Omori and Wansing.

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Author:Satoru NikiORCiDGND
Parent Title (English):Australasian journal of logic
Publisher:Victoria University of Wellington
Place of publication:Wellington
Document Type:Article
Date of Publication (online):2024/05/29
Date of first Publication:2024/05/23
Publishing Institution:Ruhr-Universität Bochum, Universitätsbibliothek
Tag:ConLog, Projekt ID: 101018280; Contradictory logics; First-degree entailment; Negation incompleteness; Negation inconsistency; Non-deterministic semantics
First Page:64
Last Page:90
ConLog, Projekt ID: 101018280
Artikel DOI des Verlages: https://doi.org/10.26686/ajl.v21i2.8202 (nicht auflösbar)
Relation (DC):info:eu-repo/grantAgreement/EC/H2020/101018280
Institutes/Facilities:Institut für Philosophie I
Dewey Decimal Classification:Philosophie und Psychologie / Philosophie
faculties:Fakultät für Philosophie und Erziehungswissenschaft
Licence (English):License LogoCreative Commons - CC BY-NC 4.0 - Attribution-NonCommercial 4.0 International