### Abstract

Original language | English |
---|---|

Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Journal of philosophical logic |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- Belnap-Dunn logic
- Gentzen calculi
- Multiple tree calculi
- Exactly true logic

### Cite this

*Journal of philosophical logic*, 1-15.

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*Journal of philosophical logic*, pp. 1-15.

**A Gentzen Calculus for Nothing but the Truth.** / Wintein, S.; Muskens, Reinhard.

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

TY - JOUR

T1 - A Gentzen Calculus for Nothing but the Truth

AU - Wintein, S.

AU - Muskens, Reinhard

N1 - Online first

PY - 2015

Y1 - 2015

N2 - In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic, an interesting variation upon the four-valued logic for first-degree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbert-style axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show that a calculus for the Belnap-Dunn logic we have defined earlier can in fact be reused for the purpose of characterising ETL, provided a small alteration is made—initial assignments of signs to the sentences of a sequent to be proved must be different from those used for characterising FDE. While Pietz & Rivieccio define ETL on the language of classical propositional logic we also study its consequence relation on an extension of this language that is functionally complete for the underlying four truth values. On this extension the calculus gets a multiple-tree character—two proof trees may be needed to establish one proof.

AB - In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic, an interesting variation upon the four-valued logic for first-degree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbert-style axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show that a calculus for the Belnap-Dunn logic we have defined earlier can in fact be reused for the purpose of characterising ETL, provided a small alteration is made—initial assignments of signs to the sentences of a sequent to be proved must be different from those used for characterising FDE. While Pietz & Rivieccio define ETL on the language of classical propositional logic we also study its consequence relation on an extension of this language that is functionally complete for the underlying four truth values. On this extension the calculus gets a multiple-tree character—two proof trees may be needed to establish one proof.

KW - Belnap-Dunn logic

KW - Gentzen calculi

KW - Multiple tree calculi

KW - Exactly true logic

M3 - Article

SP - 1

EP - 15

JO - Journal of philosophical logic

JF - Journal of philosophical logic

SN - 0022-3611

ER -