### Abstract

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

Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Studia Logica |

Early online date | 21 Sep 2014 |

DOIs | |

Publication status | Published - 2014 |

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### Keywords

- Four-valued logic; Bifacial logic; Analytic tableaux

### Cite this

*Studia Logica*, 1-14. https://doi.org/10.1007/s11225-014-9578-8

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*Studia Logica*, pp. 1-14. https://doi.org/10.1007/s11225-014-9578-8

**From Bi-facial Truth to Bi-facial Proofs.** / Wintein, S.; Muskens, R.A.

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

TY - JOUR

T1 - From Bi-facial Truth to Bi-facial Proofs

AU - Wintein, S.

AU - Muskens, R.A.

N1 - Online first

PY - 2014

Y1 - 2014

N2 - In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of these logics is left for further work. In this paper, based on our previous work on a functionally complete extension of Belnap’s logic, we present a sound and complete tableau calculus for these logics. It crucially exploits the Cartesian nature of the four values, which is reflected in the fact that each proof consists of two tableaux. The bi-facial notion of truth of Z&S is thus augmented with a bi-facial notion of proof. We also provide translations between the logics for semi-classical negation and classical logic and show that an argument is valid in a logic for semi-classical negation just in case its translation is valid in classical logic.

AB - In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of these logics is left for further work. In this paper, based on our previous work on a functionally complete extension of Belnap’s logic, we present a sound and complete tableau calculus for these logics. It crucially exploits the Cartesian nature of the four values, which is reflected in the fact that each proof consists of two tableaux. The bi-facial notion of truth of Z&S is thus augmented with a bi-facial notion of proof. We also provide translations between the logics for semi-classical negation and classical logic and show that an argument is valid in a logic for semi-classical negation just in case its translation is valid in classical logic.

KW - Four-valued logic; Bifacial logic; Analytic tableaux

U2 - 10.1007/s11225-014-9578-8

DO - 10.1007/s11225-014-9578-8

M3 - Article

SP - 1

EP - 14

JO - Studia Logica

JF - Studia Logica

SN - 0039-3215

ER -