Double Negation as Minimal Negation-Reference-Cited by-同舟云学术

Double Negation as Minimal Negation

Published:2023-11-11 Issue:5 Volume:32 Page:861-886
ISSN:0925-8531
Container-title:Journal of Logic, Language and Information
language:en
Short-container-title:J of Log Lang and Inf

Author:

Niki Satoru^ORCID

Abstract

AbstractN. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and intuitionistic negation, respectively. A consequence of this is that the systems prove contradictions but are non-trivial. The present paper aims at giving insights into this phenomenon by investigating subsystems of Kamide’s logics, with a focus on a system in which the double negation behaves as the negation of minimal logic. We establish the negation inconsistency of the system and embeddability of contradictions from other systems. In addition, we attempt at an informational interpretation of the negation using the dimathematical framework of H. Wansing.

Funder

HORIZON EUROPE European Research Council

Ruhr-Universität Bochum

Publisher

Springer Science and Business Media LLC

Subject

Linguistics and Language,Philosophy,Computer Science (miscellaneous)

Link

https://link.springer.com/content/pdf/10.1007/s10849-023-09413-1.pdf

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