Finite Hilbert Systems for Weak Kleene Logics

Vitor Greati; Sérgio Marcelino; Umberto Rivieccio

doi:10.1007/s11225-023-10079-w

Finite Hilbert Systems for Weak Kleene Logics

Vitor Greati^*
, Sérgio Marcelino
, Umberto Rivieccio

^*Corresponding author for this work

Fundamental Computing

Research output: Contribution to journal › Article › Academic › peer-review

1 Citation (Scopus)

102 Downloads (Pure)

Abstract

Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.

Original language	English
Pages (from-to)	1215-1241
Number of pages	27
Journal	Studia Logica
Volume	112
Early online date	16-Mar-2024
DOIs	https://doi.org/10.1007/s11225-023-10079-w
Publication status	Published - Dec-2024

Keywords

Bochvar–Kleene
Containment logics
Hilbert-style systems
Multiple-conclusion logics
Paraconsistent Weak Kleene

Access to Document

10.1007/s11225-023-10079-wLicence: CC BY

Finite Hilbert Systems for Weak Kleene LogicsFinal publisher's version, 568 KBLicence: CC BY

Handle.net

Persistent link

Cite this

@article{52aa1fc722f943f198f7b8de62837d6b,

title = "Finite Hilbert Systems for Weak Kleene Logics",

abstract = "Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.",

keywords = "Bochvar–Kleene, Containment logics, Hilbert-style systems, Multiple-conclusion logics, Paraconsistent Weak Kleene",

author = "Vitor Greati and S{\'e}rgio Marcelino and Umberto Rivieccio",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",

year = "2024",

month = dec,

doi = "10.1007/s11225-023-10079-w",

language = "English",

volume = "112",

pages = "1215--1241",

journal = "Studia Logica",

issn = "0039-3215",

publisher = "Springer",

}

TY - JOUR

T1 - Finite Hilbert Systems for Weak Kleene Logics

AU - Greati, Vitor

AU - Marcelino, Sérgio

AU - Rivieccio, Umberto

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/12

Y1 - 2024/12

N2 - Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.

AB - Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.

KW - Bochvar–Kleene

KW - Containment logics

KW - Hilbert-style systems

KW - Multiple-conclusion logics

KW - Paraconsistent Weak Kleene

UR - https://www.scopus.com/pages/publications/85187920912

U2 - 10.1007/s11225-023-10079-w

DO - 10.1007/s11225-023-10079-w

M3 - Article

AN - SCOPUS:85187920912

SN - 0039-3215

VL - 112

SP - 1215

EP - 1241

JO - Studia Logica

JF - Studia Logica

ER -

Finite Hilbert Systems for Weak Kleene Logics

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Cite this