A map of dependencies among three-valued logics - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Information Sciences Année : 2013

A map of dependencies among three-valued logics

Résumé

Three-valued logics arise in several fields of computer science, both inspired by concrete problems (such as in the management of the null value in databases) and theoretical considerations. Several three-valued logics have been defined. They differ by their choice of basic connectives, hence also from a syntactic and proof-theoretic point of view. Different interpretations of the third truth value have also been suggested. They often carry an epistemic flavor. In this work, relationships between logical connectives on three-valued functions are explored. Existing theorems of functional completeness have laid bare some of these links, based on specific connectives. However we try to draw a map of such relationships between conjunctions, negations and implications that extend Boolean ones. It turns out that all reasonable connectives can be defined from a few of them and so all known three-valued logics appear as a fragment of only one logic. These results can be instrumental when choosing, for each application context, the appropriate fragment where the basic connectives make full sense, based on the appropriate meaning of the third truth-value.
Fichier principal
Vignette du fichier
Ciucci_12771.pdf (941.99 Ko) Télécharger le fichier
Ciucci_12771_corrigendum.pdf (116.32 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01122868 , version 1 (04-03-2015)

Identifiants

Citer

Davide Ciucci, Didier Dubois. A map of dependencies among three-valued logics. Information Sciences, 2013, 250, pp.162-177. ⟨10.1016/j.ins.2013.06.040⟩. ⟨hal-01122868⟩
167 Consultations
1666 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More