On three-valued presentations of classical logic - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue The review of symbolic logic Année : 2023

On three-valued presentations of classical logic

Résumé

Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations st, ss, tt, ss inter tt, and ts, when the connectives are negation, conjunction, and disjunction. For ts and ss inter tt the answer is trivial (no scheme works), and for ss and tt it is straightforward (they are the collapsible schemes, in which the middle value acts like one of the classical values). For st, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible.
Fichier principal
Vignette du fichier
2312.16035.pdf (298.49 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04366457 , version 1 (08-01-2024)

Identifiants

Citer

Bruno da Ré, Damian Szmuc, Emmanuel Chemla, Paul Égré. On three-valued presentations of classical logic. The review of symbolic logic, In press, ⟨10.48550/arXiv.2312.16035⟩. ⟨hal-04366457⟩
35 Consultations
25 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More