# An Extended Paradefinte Belnap–Dunn Logic that is Embeddable into Classical Logic and Vice Versa

### Norihiro Kamide

#### Abstract

In this study, an extended paradefinite Belnap–Dunn logic (PBD) is introduced as a Gentzen-type sequent calculus. The logic PBD is an extension of Belnap–Dunn logic as well as a modified subsystem of Arieli, Avron, and Zamansky’s ideal four-valued paradefinite logic known as 4CC. The logic PBD is formalized on the basis of the idea of De and Omori’s characteristic axiom scheme for an extended Belnap–Dunn logic with classical negation (BD+), even though PBD has no classical negation connective but can simulate classical negation. Theorems for syntactically and semantically embedding PBD into a Gentzen-type sequent calculus for classical logic and vice versa are proved. The cut-elimination and completeness theorems for PBD are obtained via these embedding theorems.

Download#### Paper Citation

#### in Harvard Style

Kamide N. (2019). **An Extended Paradefinte Belnap–Dunn Logic that is Embeddable into Classical Logic and Vice Versa**.In *Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-350-6, pages 377-387. DOI: 10.5220/0007251603770387

#### in Bibtex Style

@conference{icaart19,

author={Norihiro Kamide},

title={An Extended Paradefinte Belnap–Dunn Logic that is Embeddable into Classical Logic and Vice Versa},

booktitle={Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2019},

pages={377-387},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007251603770387},

isbn={978-989-758-350-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - An Extended Paradefinte Belnap–Dunn Logic that is Embeddable into Classical Logic and Vice Versa

SN - 978-989-758-350-6

AU - Kamide N.

PY - 2019

SP - 377

EP - 387

DO - 10.5220/0007251603770387